login
A333816
Number of ways to write n as the difference of two hexagonal numbers.
6
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
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 *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 06 2020
STATUS
approved