n’th Pentagonal Number
Given an integer n, find the nth Pentagonal number. The first three pentagonal numbers are 1, 5, and 12 (Please see below diagram).
The n’th pentagonal number Pn is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots when the pentagons are overlaid so that they share one vertex [Source Wiki]
Input: n = 1 Output: 1 Input: n = 2 Output: 5 Input: n = 3 Output: 12
In general, a polygonal number (triangular number, square number, etc) is a number represented as dots or pebbles arranged in the shape of a regular polygon. The first few pentagonal numbers are: 1, 5, 12, etc.
If s is the number of sides in a polygon, the formula for the nth s-gonal number P (s, n) is
nth s-gonal number P(s, n) = (s - 2)n(n-1)/2 + n If we put s = 5, we get n'th Pentagonal number Pn = 3*n*(n-1)/2 + n
Below are the implementations of the above idea in different programming languages.
10th Pentagonal Number is = 145
Time Complexity: O(1)
Auxiliary Space: O(1)
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