A333816 Number of ways to write n as the difference of two hexagonal numbers.

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

Offset: 1

Author

Ilya Gutkovskiy, Apr 06 2020

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000384, A001227, A034178, A333815, A333817, A333818, A334035.

Programs

Mathematica

nmax = 92; CoefficientList[Series[Sum[x^(k (2 k - 1))/(1 - x^(4 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
nmax = 92; Rest[CoefficientList[Series[Sum[x^(k*(2*k - 1))/(1 - x^(4*k)), {k, 1, 1 + Sqrt[nmax/2]}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Apr 19 2020 *)

Formula

G.f.: Sum_{k>=1} x^(k*(2*k - 1)) / (1 - x^(4*k)).

G.f.: Sum_{i>=0} Sum_{j>=i} Product_{k=i..j} x^(4*k + 1).