[seqfan] On generalized pentagonal numbers ...

[Peter Luschny]

... this is a nice reading: http://fredrikj.net/blog/2016/08/additional-results/
For example:

Theorem 5. Every generalised pentagonal number c > 5 is the sum of a
smaller one and twice a
smaller one, that is, there are generalised pentagonal numbers a, b <
c such that c = 2a + b.

More in depth: http://arxiv.org/abs/1608.06810

Cheers,
Peter