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.

A035452 Number of partitions of n into parts 8k+1 or 8k+6.

This page as a plain text file.
%I A035452 #13 Aug 04 2020 08:45:31
%S A035452 1,1,1,1,1,2,2,2,3,3,3,4,4,5,6,6,7,9,9,10,11,12,14,16,17,19,21,23,25,
%T A035452 28,31,34,37,41,44,49,53,57,63,69,74,82,88,95,104,112,121,133,142,154,
%U A035452 167,179,193,209,224,243,261,280,301,324,347,373,400,430,460,494,528
%N A035452 Number of partitions of n into parts 8k+1 or 8k+6.
%H A035452 Robert Price, <a href="/A035452/b035452.txt">Table of n, a(n) for n = 1..1000</a>
%F A035452 a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(3/4) * Gamma(1/8) / (4 * 2^(15/16) * 3^(3/16) * Pi^(9/8) * n^(11/16)). - _Vaclav Kotesovec_, Aug 26 2015
%t A035452 nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+1))*(1 - x^(8k+6))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 26 2015 *)
%t A035452 nmax = 60; kmax = nmax/8;
%t A035452 s = Flatten[{Range[0, kmax]*8 + 1}~Join~{Range[0, kmax]*8 + 6}];
%t A035452 Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* _Robert Price_, Aug 03 2020 *)
%Y A035452 Cf. A035683.
%K A035452 nonn
%O A035452 1,6
%A A035452 _Olivier Gérard_