A333817 G.f.: Sum_{k>=1} x^(k*(5*k - 3)/2) / (1 - x^(5*k)).

1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1

Offset: 1

Author

Ilya Gutkovskiy, Apr 06 2020

Keywords

• nonn

Comments

Number of ways to write n as the difference of two heptagonal numbers.

Crossrefs

Cf. A000566, A001227, A034178, A333815, A333816, A333818.

Programs

Mathematica

nmax = 93; CoefficientList[Series[Sum[x^(k (5 k - 3)/2)/(1 - x^(5 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

G.f.: Sum_{i>=0} Sum_{j>=i} Product_{k=i..j} x^(5*k + 1).