Definition:Second Pentagonal Number/Definition 2

Definition

The second pentagonal numbers are the integers obtained from formula:

$\map {P'} n = \dfrac {n \paren {3 n + 1} } 2$

for $n = 0, 1, 2, \ldots$

Sequence

The sequence of second pentagonal numbers, for $n \in \Z_{\ge 0}$, begins:

$0, 2, 7, 15, 26, 40, 57, 77, 100, 126, 155, 187, \ldots$

Also see

• Equivalence of Definitions of Second Pentagonal Number

• Results about second pentagonal numbers can be found here.