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.

A035441 Number of partitions of n into parts 8k or 8k+1.

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%I A035441 #14 Aug 03 2020 01:32:41
%S A035441 1,1,1,1,1,1,1,2,3,3,3,3,3,3,3,5,7,8,8,8,8,8,8,11,15,17,18,18,18,18,
%T A035441 18,23,30,35,37,38,38,38,38,45,57,66,71,73,74,74,74,85,104,121,131,
%U A035441 136,138,139,139,154,184,212,231,241,246,248,249,271,316,363,396,416
%N A035441 Number of partitions of n into parts 8k or 8k+1.
%H A035441 Robert Price, <a href="/A035441/b035441.txt">Table of n, a(n) for n = 1..1000</a>
%F A035441 a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(9/8) * 2^(7/16) / (3^(5/16) * Pi^(7/8) * n^(13/16)). - _Vaclav Kotesovec_, Aug 26 2015
%t A035441 nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+8))*(1 - x^(8k+1))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 26 2015 *)
%t A035441 nmax = 68; kmax = nmax/8;
%t A035441 s = Flatten[{Range[0, kmax]*8}~Join~{Range[0, kmax]*8 + 1}];
%t A035441 Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* _Robert Price_, Aug 02 2020 *)
%Y A035441 Cf. A035672.
%K A035441 nonn
%O A035441 1,8
%A A035441 _Olivier Gérard_