Python Program to Find nth Decagonal Number

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Decagonal Number:

A decagonal number is a figurate number that extends the triangle and square number concepts to the decagon (a ten-sided polygon).  The nth decagonal number counts the number of dots in a pattern of n nested decagons, each of which has a shared corner.

Formula to generate a Decagonal Number:

D(n) = 4*n^2 - 3*n

Given a number and the task is to find the decagonal number of a given number.

Examples:

Example1:

Input:

Given Number = 4

Output:

The decagonal number of a given number { 4 } = 
52

Example2:

Input:

Given Number = 10

Output:

The decagonal number of a given number { 10 } = 
370

Program to Find nth Decagonal Number in Python

Method #1: Using Mathematical Formula (Static Input)

Approach:

  • Create a function say Find_DecagonalNum() which accepts the given number as an argument and returns the decagonal number of the given number.
  • Inside the function, calculate the decagonal number of a given number using the above given mathematical formula and return it.
  • Give the number as static input and store it in a variable.
  • Pass the given number to the Find_DecagonalNum() function store it in another variable.
  • Print the decagonal number of a given number.
  • The Exit of the Program.

Below is the implementation:

# Create a function say Find_DecagonalNum() which accepts the given number as an
# argument and returns the decagonal number of the given number.


def Find_DecagonalNum(gvn_num):
    # Inside the function, calculate the decagonal number of a given number using the
    # above given mathematical formula and return it.
    return(4*gvn_num*gvn_num - 3*gvn_num)


# Give the number as static input and store it in a variable.
gvn_num = 4
# Pass the given number to the Find_DecagonalNum() function store it in another
# variable.
rslt = Find_DecagonalNum(gvn_num)
# Print the decagonal number of a given number.
print("The decagonal number of a given number {", gvn_num, "} = ")
print(rslt)

Output:

The decagonal number of a given number { 4 } = 
52

Method #2: Using Mathematical Formula (User Input)

Approach:

  • Create a function say Find_DecagonalNum() which accepts the given number as an argument and returns the decagonal number of the given number.
  • Inside the function, calculate the decagonal number of a given number using the above given mathematical formula and return it.
  • Give the number as user input using the int(input()) function and store it in a variable.
  • Pass the given number to the Find_DecagonalNum() function store it in another variable.
  • Print the decagonal number of a given number.
  • The Exit of the Program.

Below is the implementation:

# Create a function say Find_DecagonalNum() which accepts the given number as an
# argument and returns the decagonal number of the given number.


def Find_DecagonalNum(gvn_num):
    # Inside the function, calculate the decagonal number of a given number using the
    # above given mathematical formula and return it.
    return(4*gvn_num*gvn_num - 3*gvn_num)


# Give the number as user input using the int(input()) function and store it in a variable.
gvn_num = int(input("Enter some random number = "))
# Pass the given number to the Find_DecagonalNum() function store it in another
# variable.
rslt = Find_DecagonalNum(gvn_num)
# Print the decagonal number of a given number.
print("The decagonal number of a given number {", gvn_num, "} = ")
print(rslt)

Output:

Enter some random number = 10
The decagonal number of a given number { 10 } = 
370