C program to find Decagonal Number

A decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). The n^th decagonal numbers counts the number of dots in a pattern of n nested decagons, all sharing a common corner, where the i^th decagon in the pattern has sides made of i dots spaced one unit apart from each other. The n-th decagonal number is given by the formula D(n)=4n²-3n; The first few decagonal numbers are: 0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242…… Examples:

Input : n = 2
Output : 10

Input : n = 5
Output : 85

Input : n = 7
Output: 175

CPP

// C program to find nth decagonal number
#include <stdio.h>
#include <stdlib.h>

// Finding the nth  Decagonal Number
int decagonalNum(int n)
{
    return (4 * n * n - 3 * n);
}

// Driver program to test above function
int main()
{
    int n = 10;
    printf("Decagonal Number is = %d",
           decagonalNum(n));

    return 0;
}

Output:

Decagonal Number is = 370

Time complexity: O(1) as constant operations are done

Auxiliary space: O(1)

References : Mathworld