polygonal number

Arithmetic progression can have first term one and common difference n - 2, where n is number of polygon sides {polygonal number}.

n can be three, so sequence is 1, 3, 6, 10, 15, 21, ... {triangular number}.

n can be four, so sequence is 1, 4, 9, 16, 25, ... {square number, polygonal}.

n can be five, so sequence is 1, 5, 12, 22, ... {pentagonal number}.

For n, sequence is l, n, 3*n - 3, 6*n - 8, ... {n-gonal number}.

general

In general, 0.5 * (r + 1) * (r*n - 2*r + 2), where r is whole number, makes polygonal numbers.

Date Modified: 2022.0224