Definition:Polygonal Number/Examples

Triangular Numbers
When $k = 3$, the recurrence relation is:

See Triangular Number.

Square Numbers
When $k = 4$, the recurrence relation is:

See Square Number.

Square numbers are of course better known as:
 * $S_n = n^2$

Pentagonal Numbers
When $k = 5$, the recurrence relation is:

See Pentagonal Number.

Hexagonal Numbers
When $k = 6$, the recurrence relation is:

See Hexagonal Number.