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.

A363977 Expansion of Sum_{k>0} x^k / (1 - x^(4*k))^3.

This page as a plain text file.
%I A363977 #10 Jun 30 2023 15:35:43
%S A363977 1,1,1,1,4,1,1,1,7,4,1,1,11,1,4,1,16,7,1,4,22,1,1,1,32,11,7,1,37,4,1,
%T A363977 1,46,16,4,7,56,1,11,4,67,22,1,1,88,1,1,1,92,32,16,11,106,7,4,1,121,
%U A363977 37,1,4,137,1,28,1,167,46,1,16,172,4,1,7,191,56,32,1,211,11,1,4,238,67,1
%N A363977 Expansion of Sum_{k>0} x^k / (1 - x^(4*k))^3.
%F A363977 G.f.: Sum_{k>0} k*(k+1)/2 * x^(4*k-3) / (1 - x^(4*k-3)).
%F A363977 a(n) = Sum_{d|n, d==1 mod 4} binomial((d+3)/4+1,2).
%t A363977 a[n_] := DivisorSum[n, Binomial[(#+3)/4+1,2] &, Mod[#, 4] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Jun 30 2023 *)
%o A363977 (PARI) a(n) = sumdiv(n, d, (d%4==1)*binomial((d+3)/4+1, 2));
%Y A363977 Cf. A001826, A363903.
%Y A363977 Cf. A363972.
%K A363977 nonn
%O A363977 1,5
%A A363977 _Seiichi Manyama_, Jun 30 2023