cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A333816 #18 Apr 19 2020 07:55:06
%S A333816 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,
%T A333816 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,
%U A333816 1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,2,1,1,0,1,1,1,1
%N A333816 Number of ways to write n as the difference of two hexagonal numbers.
%H A333816 Vaclav Kotesovec, <a href="/A333816/b333816.txt">Table of n, a(n) for n = 1..10000</a>
%F A333816 G.f.: Sum_{k>=1} x^(k*(2*k - 1)) / (1 - x^(4*k)).
%F A333816 G.f.: Sum_{i>=0} Sum_{j>=i} Product_{k=i..j} x^(4*k + 1).
%t A333816 nmax = 92; CoefficientList[Series[Sum[x^(k (2 k - 1))/(1 - x^(4 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A333816 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 *)
%Y A333816 Cf. A000384, A001227, A034178, A333815, A333817, A333818, A334035.
%K A333816 nonn
%O A333816 1,45
%A A333816 _Ilya Gutkovskiy_, Apr 06 2020