Definition:Generalized Pentagonal Number/Definition 1

Definition

Recall the sequence of pentagonal numbers:

$0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, \ldots$

and the sequence of second pentagonal numbers:

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

The sequence of generalized pentagonal numbers consists of the elements of both of these sequences merged and arranged into ascending order.

Sequence

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

$GP_n = 0, 1, 2, 5, 7, 12, 15, 22, 26, 35, 40, 51, 57, 70, 77, 92, 100, \ldots$

Also see

• Equivalence of Definitions of Generalized Pentagonal Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $22$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $22$