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)=4n^{2}-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……

Input : n = 2 Output : 10 Input : n = 5 Output : 85 Input : n = 7 Output: 175

`// 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; ` `} ` |

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**Output:**

Decagonal Number is = 370

**References :** Mathworld

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