Python - Pyramid Patterns

Pattern-34 starts a new category: Pyramid Patterns.

A normal pyramid follows two important formulas:

Leading Spaces = n - i

Values = 2 * i - 1

For n = 5:

i	Spaces	2*i-1
1	4	1
2	3	3
3	2	5
4	1	7
5	0	9

Therefore the number of values follows the odd-number sequence:

1, 3, 5, 7, 9, ...

Pattern-34 creates a pyramid using stars.

Output

    *
   * * *
  * * * * *
 * * * * * * *
* * * * * * * * *

The source program uses:

"* " * (2*i-1)

So every row contains an odd number of stars.

The expression:

" " * (n-i)

controls the leading spaces.

The expression:

"* " * (2*i-1)

controls the number of stars.

For each row:

i = 1 → 2(1)-1 = 1
i = 2 → 2(2)-1 = 3
i = 3 → 2(3)-1 = 5
i = 4 → 2(4)-1 = 7
i = 5 → 2(5)-1 = 9

Row	Spaces	Stars
1	4	1
2	3	3
3	2	5
4	1	7
5	0	9

Output

    1
   2 2 2
  3 3 3 3 3
 4 4 4 4 4 4 4
5 5 5 5 5 5 5 5 5

The row number is repeated an odd number of times.

The current number is:

i

It is converted into a string:

str(i)

A space is added:

str(i) + " "

Then it is repeated:

2*i - 1

Example for i = 4:

2*4 - 1
= 7

"4 " * 7

4 4 4 4 4 4 4

Output

    A
   B B B
  C C C C C
 D D D D D D D
E E E E E E E E E

The alphabet changes according to the row.

The repetition count follows:

1, 3, 5, 7, 9

The alphabet formula is:

chr(64+i)

Therefore:

i = 1 → A
i = 2 → B
i = 3 → C
i = 4 → D
i = 5 → E

The repetition count is:

2*i - 1

For row 3:

Character = C

Repetitions =
2*3 - 1
= 5

C C C C C

Output

    A
   C C C
  E E E E E
 G G G G G G G
I I I I I I I I I

This pattern skips one alphabet after every row.

A → C → E → G → I

The important formula is:

chr(63 + 2*i)

For each row:

i = 1

63 + 2
= 65

chr(65)
= A

i = 2

63 + 4
= 67

chr(67)
= C

i = 3

63 + 6
= 69

chr(69)
= E

Therefore:

A, C, E, G, I

Again, the repetition count is:

2*i - 1

Pattern-38 is more advanced because every row contains an increasing and decreasing alphabet sequence.

Output

    A
   A B A
  A B C B A
 A B C D C B A
A B C D E D C B A

This is an alphabet palindrome pattern.

Each row reads the same from left to right and right to left.

The first inner loop is:

for j in range(65,65+i):
    print(chr(j),end=" ")

It prints alphabets in increasing order.

For i = 5:

65 → A
66 → B
67 → C
68 → D
69 → E

A B C D E

The second inner loop is:

for k in range(63+i,64,-1):
    print(chr(k),end=" ")

It prints the remaining alphabets in reverse order.

For i = 5:

k starts at:

63 + 5
= 68

chr(68) = D

Then:

68 → D
67 → C
66 → B
65 → A

So the complete row becomes:

A B C D E + D C B A

A B C D E D C B A

i	Increasing Part	Decreasing Part	Complete Row
1	A	-	A
2	A B	A	A B A
3	A B C	B A	A B C B A
4	A B C D	C B A	A B C D C B A
5	A B C D E	D C B A	A B C D E D C B A

Output

    1
   3 2 1
  5 4 3 2 1
 7 6 5 4 3 2 1
9 8 7 6 5 4 3 2 1

Each row starts with an odd number and decreases until 1.

The starting number is:

2*i - 1

Therefore:

i = 1 → 1
i = 2 → 3
i = 3 → 5
i = 4 → 7
i = 5 → 9

The loop:

range(2*i-1,0,-1)

counts backward until 1.

For i = 4:

2*4 - 1
= 7

range(7,0,-1)

7 6 5 4 3 2 1

i	Starting Value	Output
1	1	1
2	3	3 2 1
3	5	5 4 3 2 1
4	7	7 6 5 4 3 2 1
5	9	9 8 7 6 5 4 3 2 1

Output

    A
   A B C
  A B C D E
 A B C D E F G
A B C D E F G H I

Every row starts from A.

The number of alphabets follows:

1, 3, 5, 7, 9

The alphabet loop is:

for j in range(65,65+2*i-1):

The loop always starts at ASCII:

65 → A

The number of iterations is:

2*i - 1

For row 3:

2*3 - 1
= 5

Therefore five alphabets are printed:

A B C D E

For row 5:

2*5 - 1
= 9

A B C D E F G H I

Pattern	Pyramid Content	Main Formula
34	Stars	2*i-1 stars
35	Repeated row number	i repeated 2*i-1 times
36	Repeated row alphabet	chr(64+i)
37	Odd-position alphabet	chr(63+2*i)
38	Alphabet palindrome	Increasing + decreasing alphabets
39	Reverse numbers	2*i-1 down to 1
40	Increasing alphabets	2*i-1 alphabets

The expression:

2*i - 1

generates consecutive odd numbers.

i	Calculation	Result
1	2 × 1 - 1	1
2	2 × 2 - 1	3
3	2 × 3 - 1	5
4	2 × 4 - 1	7
5	2 × 5 - 1	9

This formula is useful because a pyramid normally grows symmetrically:

        1
      3 values
    5 values
  7 values
9 values

Pattern	Leading Spaces	Main Logic
31	i-1	j = 1 to n+1-i
32	i-1	chr(65+n-i) repeated n+1-i
33	i-1	A to decreasing endpoint
34	n-i	2*i-1 stars
35	n-i	i repeated 2*i-1
36	n-i	chr(64+i) repeated 2*i-1
37	n-i	chr(63+2*i) repeated 2*i-1
38	n-i	Increasing + decreasing alphabet
39	n-i	2*i-1 down to 1
40	n-i	Print 2*i-1 alphabets from A

                         START
                           │
                           ▼
                        Read n
                           │
                           ▼
                    Outer Loop (i)
                           │
                           ▼
                  Identify Pattern
                           │
              ┌────────────┴────────────┐
              │                         │
              ▼                         ▼
        Pattern 31-33              Pattern 34-40
              │                         │
              ▼                         ▼
       Decreasing Shape               Pyramid
              │                         │
              ▼                         ▼
     Spaces = i - 1             Spaces = n - i
              │                         │
              ▼                         ▼
 Values = n + 1 - i          Values usually = 2*i-1
              │                         │
              └────────────┬────────────┘
                           │
                           ▼
                    Print Spaces
                           │
                           ▼
                   Generate Values
                           │
              ┌────────────┼────────────┐
              ▼            ▼            ▼
           Stars        Numbers      Alphabets
              │            │            │
              └────────────┴────────────┘
                           │
                           ▼
                      Print Row
                           │
                           ▼
                       Next Row
                           │
                           ▼
                          END

• Patterns 31–33 use increasing leading spaces and decreasing values.
• The common space formula for Patterns 31–33 is i-1.
• Pattern-31 always starts its number sequence from 1.
• Pattern-32 uses chr(65+n-i) to generate decreasing alphabets.
• Pattern-33 always starts its alphabet sequence from A.
• Pattern-34 begins the pyramid-pattern section.
• The most important pyramid formula is 2*i-1.
• 2*i-1 generates the sequence 1, 3, 5, 7, 9, ....
• The common leading-space formula for these increasing pyramids is n-i.
• Pattern-37 uses chr(63+2*i) to generate A, C, E, G, I....
• Pattern-38 requires two inner loops because it first increases alphabets and then decreases them.
• Pattern-39 uses a negative step -1 to print numbers in reverse order.
• Pattern-40 combines ASCII values with the 2*i-1 pyramid formula.

Pattern	Output Type	Key Concept
31	Decreasing numbers	Increasing spaces
32	Repeated decreasing alphabet	ASCII + repetition
33	Decreasing alphabet sequence	ASCII range
34	Star pyramid	2*i-1 stars
35	Number pyramid	Repeated row number
36	Alphabet pyramid	Repeated row alphabet
37	Odd alphabet pyramid	A, C, E, G, I
38	Palindrome alphabet pyramid	Forward + backward loops
39	Reverse number pyramid	Odd number to 1
40	Alphabet pyramid	2*i-1 alphabets

                    PATTERN 31-40
                          │
          ┌───────────────┴───────────────┐
          │                               │
          ▼                               ▼
     Pattern 31-33                   Pattern 34-40
          │                               │
          ▼                               ▼
 Decreasing Right-Shifted               Pyramid
          │                               │
          ▼                               ▼
 Spaces = i - 1                   Spaces = n - i
          │                               │
          ▼                               ▼
Values = n + 1 - i              Values ≈ 2*i - 1
          │                               │
     ┌────┴────┐             ┌────────────┼────────────┐
     ▼         ▼             ▼            ▼            ▼
  Numbers   Alphabets      Stars       Numbers      Alphabets
                                                    │
                                      ┌─────────────┼─────────────┐
                                      ▼             ▼             ▼
                                   Repeated     Palindrome     Sequence

Part 5 covers Pattern-41 to Pattern-50.

In this part, we will learn:

Pattern-41 → Reverse Alphabet Pyramid
Pattern-42 → Reverse-to-Forward Number Pyramid
Pattern-43 → Reverse-to-Forward Alphabet Pyramid
Pattern-44 → Palindrome Number Pyramid
Pattern-45 → Repeated Increasing Alphabet Pyramid
Pattern-46 → Descending Number Triangle
Pattern-47 → Inverted Star Pyramid
Pattern-48 → Inverted Repeated Number Pyramid
Pattern-49 → Inverted Odd Number Pyramid
Pattern-50 → Inverted Number Sequence Pattern

Important concepts used in this part are:

• Nested loops
• Increasing and decreasing ranges
• Negative step in range()
• ASCII values with chr()
• Leading spaces
• Odd-number formulas
• Two inner loops in the same row
• Increasing and inverted pyramids

Pattern-41 prints alphabets in reverse order.

The starting alphabet increases by two positions in every row.

Output

    A
   C B A
  E D C B A
 G F E D C B A
I H G F E D C B A

Observe the first alphabet of every row:

A
C
E
G
I

These are alternate alphabets.

After selecting the starting alphabet, the program prints backward until A.

Step 1 — Read Number of Rows

n=int(input("Enter the number of rows: "))

The variable n stores the number of rows.

Step 2 — Outer Loop

for i in range(1,n+1):

The outer loop controls the rows.

Step 3 — Print Leading Spaces

print(" "*(n-i),end="")

The number of spaces decreases in every row.

n = 5

i = 1 → 4 spaces
i = 2 → 3 spaces
i = 3 → 2 spaces
i = 4 → 1 space
i = 5 → 0 spaces

Step 4 — Calculate Starting Alphabet

65 + 2*i - 2

For different rows:

i = 1 → 65 → A
i = 2 → 67 → C
i = 3 → 69 → E
i = 4 → 71 → G
i = 5 → 73 → I

Step 5 — Print in Reverse Order

range(65+2*i-2,64,-1)

The value decreases by 1 until ASCII value 65.

For row 4:

Starting ASCII = 71

71 → G
70 → F
69 → E
68 → D
67 → C
66 → B
65 → A

Therefore:

G F E D C B A

i	Start ASCII	Start Character	Output
1	65	A	A
2	67	C	C B A
3	69	E	E D C B A
4	71	G	G F E D C B A
5	73	I	I H G F E D C B A

Pattern-42 creates a number pyramid using two parts.

The first part prints numbers in decreasing order and the second part prints numbers in increasing order.

Output

    0
   1 0 1
  2 1 0 1 2
 3 2 1 0 1 2 3
4 3 2 1 0 1 2 3 4

The center value of every row is:

0

The values are symmetrical around 0.

The first inner loop is:

for j in range(1,i):
    print(i-j,end=" ")

It prints decreasing values before 0.

For i = 5:

j = 1 → 5-1 = 4
j = 2 → 5-2 = 3
j = 3 → 5-3 = 2
j = 4 → 5-4 = 1

Output:

4 3 2 1

The second inner loop is:

for k in range(0,i):
    print(k,end=" ")

It prints:

0 1 2 ... i-1

For i = 5:

0 1 2 3 4

Combining both loops:

4 3 2 1 + 0 1 2 3 4

4 3 2 1 0 1 2 3 4

Row	Left Part	Right Part	Complete Output
1	-	0	0
2	1	0 1	1 0 1
3	2 1	0 1 2	2 1 0 1 2
4	3 2 1	0 1 2 3	3 2 1 0 1 2 3
5	4 3 2 1	0 1 2 3 4	4 3 2 1 0 1 2 3 4

Pattern-43 is the alphabet version of Pattern-42.

Output

    A
   B A B
  C B A B C
 D C B A B C D
E D C B A B C D E

The pattern decreases toward A and then increases again.

First Part

for j in range(1,i):
    print(chr(i-j+65),end=" ")

This prints alphabets in decreasing order.

For i = 5:

j = 1 → chr(69) → E
j = 2 → chr(68) → D
j = 3 → chr(67) → C
j = 4 → chr(66) → B

First part:

E D C B

Second Part

for k in range(0,i):
    print(chr(k+65),end=" ")

For i = 5:

k = 0 → A
k = 1 → B
k = 2 → C
k = 3 → D
k = 4 → E

Second part:

A B C D E

Complete row:

E D C B A B C D E

Feature	Pattern-42	Pattern-43
Data Type	Numbers	Alphabets
Center	0	A
Left Side	Decreasing numbers	Decreasing alphabets
Right Side	Increasing numbers	Increasing alphabets
Character Conversion	Not required	chr()

Output

    1
   1 2 1
  1 2 3 2 1
 1 2 3 4 3 2 1
1 2 3 4 5 4 3 2 1

Every row first increases from 1 to the row number and then decreases back to 1.

Therefore every row forms a numeric palindrome.

The first loop is:

for j in range(1,i+1):
    print(j,end=" ")

For row 5:

1 2 3 4 5

The second loop is:

for k in range(i-1,0,-1):
    print(k,end=" ")

The loop starts from:

i - 1

This prevents the highest value from being printed twice.

For row 5:

4 3 2 1

Complete row:

1 2 3 4 5 4 3 2 1

i	Increasing Part	Decreasing Part	Output
1	1	-	1
2	1 2	1	1 2 1
3	1 2 3	2 1	1 2 3 2 1
4	1 2 3 4	3 2 1	1 2 3 4 3 2 1
5	1 2 3 4 5	4 3 2 1	1 2 3 4 5 4 3 2 1

Output

    A
   A B A
  A B C A B
 A B C D A B C
A B C D E A B C D

Each row contains two alphabet sequences.

The first sequence prints from A to the current row alphabet.

The second sequence again starts from A, but stops one alphabet earlier.

for j in range(1,i+1):
    print(chr(64+j),end=" ")

For row 5:

j = 1 → A
j = 2 → B
j = 3 → C
j = 4 → D
j = 5 → E

Result:

A B C D E

for k in range(1,i):
    print(chr(64+k),end=" ")

For row 5:

A B C D

Therefore the complete row is:

A B C D E A B C D

The second loop uses:

range(1,i)

instead of:

range(1,i+1)

Therefore it prints one fewer alphabet.

Pattern-46 prints numbers starting from n and decreases toward smaller values.

The number of values increases row by row.

Program Logic Output for n = 5

    5
   5 4
  5 4 3
 5 4 3 2
5 4 3 2 1

The value printed is calculated using:

n + 1 - j

If n = 5:

j = 1 → 5+1-1 = 5
j = 2 → 5+1-2 = 4
j = 3 → 5+1-3 = 3
j = 4 → 5+1-4 = 2
j = 5 → 5+1-5 = 1

But the inner loop executes only i times:

range(1,i+1)

Therefore:

Row 1 → 5
Row 2 → 5 4
Row 3 → 5 4 3
Row 4 → 5 4 3 2
Row 5 → 5 4 3 2 1

Leading Spaces = n - i

Number of Values = i

Printed Value = n + 1 - j

Pattern-47 begins the inverted/decreasing pyramid section.

Output

* * * * * * * * *
 * * * * * * *
  * * * * *
   * * *
    *

The number of stars follows:

9
7
5
3
1

At the same time, leading spaces increase.

for j in range(1,num+2-i):
    print("*",end=" ")

The first loop prints:

num + 1 - i

stars.

For num = 5:

i = 1 → 5 stars
i = 2 → 4 stars
i = 3 → 3 stars
i = 4 → 2 stars
i = 5 → 1 star

for k in range(1,num+1-i):
    print("*",end=" ")

The second loop prints:

num - i

additional stars.

Therefore the total is:

(num + 1 - i) + (num - i)

= 2*num + 1 - 2*i

For num = 5:

i = 1 → 9 stars
i = 2 → 7 stars
i = 3 → 5 stars
i = 4 → 3 stars
i = 5 → 1 star

i	Spaces	First Loop	Second Loop	Total Stars
1	0	5	4	9
2	1	4	3	7
3	2	3	2	5
4	3	2	1	3
5	4	1	0	1

Output

5 5 5 5 5 5 5 5 5
 4 4 4 4 4 4 4
  3 3 3 3 3
   2 2 2
    1

The row value decreases:

5 → 4 → 3 → 2 → 1

The number of repetitions also decreases:

9 → 7 → 5 → 3 → 1

The number printed in each row is:

num + 1 - i

For num = 5:

i = 1 → 5
i = 2 → 4
i = 3 → 3
i = 4 → 2
i = 5 → 1

Two loops print the same number.

First Loop

for j in range(0,num+1-i):

Second Loop

for k in range(1,num+1-i):

Together they generate:

2*num + 1 - 2*i

values.

Therefore:

Row 1 → 9 copies of 5
Row 2 → 7 copies of 4
Row 3 → 5 copies of 3
Row 4 → 3 copies of 2
Row 5 → 1 copy of 1

Output

9 9 9 9 9 9 9 9 9
 7 7 7 7 7 7 7
  5 5 5 5 5
   3 3 3
    1

This pattern prints decreasing odd numbers.

9
7
5
3
1

The number itself is also repeated the same number of times.

The most important expression is:

2*num + 1 - 2*i

For num = 5:

i = 1

2*5 + 1 - 2*1
= 10 + 1 - 2
= 9

i = 2

11 - 4
= 7

i = 3

11 - 6
= 5

i = 4

11 - 8
= 3

i = 5

11 - 10
= 1

Therefore the values are:

9, 7, 5, 3, 1

i	Spaces	Value	Repetitions
1	0	9	9
2	1	7	7
3	2	5	5
4	3	3	3
5	4	1	1

Pattern-50 prints an inverted sequence of numbers.

Output

1 2 3 4 5 6 7
 1 2 3 4 5
  1 2 3
   1

The number of printed values decreases by two after every row.

7 → 5 → 3 → 1

This pattern uses two inner loops to construct every row.

The first inner loop is:

for j in range(1,num+2-i):
    print(j,end=" ")

It prints an increasing sequence starting from 1.

For example, when num = 4:

i = 1 → 1 2 3 4
i = 2 → 1 2 3
i = 3 → 1 2
i = 4 → 1

The second inner loop is:

for k in range(2,num+2-i):
    print(num+k-i,end=" ")

It prints the remaining increasing numbers required to complete the row.

For num = 4 and i = 1:

First loop:
1 2 3 4

Second loop:

k = 2 → 4 + 2 - 1 = 5
k = 3 → 4 + 3 - 1 = 6
k = 4 → 4 + 4 - 1 = 7

Therefore:

1 2 3 4 5 6 7

For row 2:

First loop:
1 2 3

Second loop:
4 5

Complete:
1 2 3 4 5

For row 3:

1 2 3

For row 4:

1

For num = 4:

i	Spaces	First Loop	Second Loop	Complete Row
1	0	1 2 3 4	5 6 7	1 2 3 4 5 6 7
2	1	1 2 3	4 5	1 2 3 4 5
3	2	1 2	3	1 2 3
4	3	1	-	1

Pattern	Type	Main Logic
41	Reverse Alphabet	Odd-position alphabet down to A
42	Number Symmetry	Decrease to 0, then increase
43	Alphabet Symmetry	Decrease to A, then increase
44	Number Palindrome	Increase and then decrease
45	Repeated Alphabet Sequence	Two increasing alphabet loops
46	Descending Numbers	Start from n and decrease

Pattern	Type	Row Size
47	Stars	9, 7, 5, 3, 1
48	Repeated Numbers	9, 7, 5, 3, 1
49	Repeated Odd Numbers	9, 7, 5, 3, 1
50	Increasing Number Sequence	7, 5, 3, 1 for num = 4

Increasing Pyramid Spaces

n - i

Used in Patterns 41–46.

Inverted Pyramid Spaces

i - 1

Used in Patterns 47–50.

Pattern-41 Starting Alphabet

65 + 2*i - 2

Pattern-46 Printed Number

n + 1 - j

Inverted Odd Row Size

2*num + 1 - 2*i

For num = 5, this generates:

9, 7, 5, 3, 1

Pattern-49 Printed Value

2*num + 1 - 2*i

Increasing Pyramid

Leading spaces decrease while values increase.

    *
   * * *
  * * * * *
 * * * * * * *
* * * * * * * * *

Typical space formula:

n - i

Inverted Pyramid

Leading spaces increase while values decrease.

* * * * * * * * *
 * * * * * * *
  * * * * *
   * * *
    *

Typical space formula:

i - 1

This relationship is very important when solving pattern-programming questions.

                         START
                           │
                           ▼
                      Read n / num
                           │
                           ▼
                       Outer Loop
                           │
                           ▼
                 Calculate Row Number
                           │
                           ▼
                    Print Spaces
                           │
             ┌─────────────┴─────────────┐
             │                           │
             ▼                           ▼
      Increasing Pyramid          Inverted Pyramid
       Pattern 41-46              Pattern 47-50
             │                           │
             ▼                           ▼
      Spaces Decrease              Spaces Increase
         n - i                       i - 1
             │                           │
             ▼                           ▼
      Values Increase              Values Decrease
             │                           │
             └─────────────┬─────────────┘
                           │
                           ▼
                  Execute Inner Loop
                           │
                    ┌──────┴──────┐
                    ▼             ▼
               First Part     Second Part
                    │             │
                    └──────┬──────┘
                           ▼
                       Print Row
                           │
                           ▼
                       Next Row
                           │
                           ▼
                          END

• Pattern-41 uses ASCII values to generate alternate starting alphabets A, C, E, G, I.
• A negative step such as -1 is used when values must move backward.
• Pattern-42 combines decreasing and increasing number sequences.
• Pattern-43 applies the same idea using alphabets.
• Pattern-44 is a proper number palindrome because the second half is the reverse of the first half without repeating the center value.
• Pattern-45 uses two increasing alphabet loops.
• Pattern-46 always begins its sequence from n.
• Pattern-47 starts the inverted pyramid patterns in this section.
• In an inverted pyramid, spaces generally increase while the number of values decreases.
• Patterns 47–49 use two loops to create odd-sized rows.
• The sequence 9, 7, 5, 3, 1 can be generated using 2*num+1-2*i when num = 5.
• Pattern-48 repeats the value num+1-i.
• Pattern-49 uses the same odd-number formula both for the printed value and the effective row width.
• Pattern-50 creates decreasing odd-sized rows of consecutive numbers.
• end="" is important when spaces and pattern values must continue on the same line.
• print() after the inner loops moves the cursor to the next row.

Pattern	Pattern Type	Key Concept
41	Reverse Alphabet Pyramid	ASCII + reverse range
42	Number Symmetry Pyramid	Decrease → 0 → Increase
43	Alphabet Symmetry Pyramid	Decrease → A → Increase
44	Number Palindrome	Forward + backward loops
45	Repeated Alphabet Sequence	Two forward loops
46	Descending Number Triangle	n+1-j
47	Inverted Star Pyramid	Odd decreasing width
48	Inverted Number Pyramid	Repeated decreasing value
49	Inverted Odd Number Pyramid	2*num+1-2*i
50	Inverted Number Sequence	Two increasing number loops

                     PATTERN 41-50
                           │
          ┌────────────────┴────────────────┐
          │                                 │
          ▼                                 ▼
     Pattern 41-46                    Pattern 47-50
   Advanced Pyramids                Inverted Patterns
          │                                 │
     Spaces = n-i                      Spaces = i-1
          │                                 │
     ┌────┼────────────┐              ┌─────┼───────────┐
     ▼    ▼            ▼              ▼     ▼           ▼
 Alphabet Number   Palindrome        Star  Number   Sequence
     │    │            │              │     │           │
     │    │            │              │     │           │
    41   42,46         44             47    48,49        50
     │
     ├── Pattern 43 → Alphabet Symmetry
     │
     └── Pattern 45 → Repeated Alphabet Sequence