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

1,45

Links

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

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).

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 *)

Crossrefs

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

Sequence in context: A298426 A130068 A316825 * A363709 A246398 A051699

Adjacent sequences: A333813 A333814 A333815 * A333817 A333818 A333819

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 06 2020

Status

approved