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.

A035943 Number of partitions of n into parts not of the form 9k, 9k+4 or 9k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 3 are greater than 1.

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%I A035943 #16 May 11 2018 04:21:52
%S A035943 1,1,2,3,4,5,8,10,14,18,24,30,40,49,63,78,98,120,150,182,224,271,330,
%T A035943 396,480,572,687,817,974,1151,1367,1608,1898,2226,2614,3053,3573,4157,
%U A035943 4844,5620,6524,7544,8731,10066,11611,13353,15356,17612,20203,23112
%N A035943 Number of partitions of n into parts not of the form 9k, 9k+4 or 9k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 3 are greater than 1.
%C A035943 Case k=4,i=4 of Gordon Theorem.
%D A035943 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%H A035943 Seiichi Manyama, <a href="/A035943/b035943.txt">Table of n, a(n) for n = 0..1000</a>
%F A035943 a(n) ~ cos(Pi/18) * exp(2*Pi*sqrt(n)/3) / (3*sqrt(3)*n^(3/4)). - _Vaclav Kotesovec_, Nov 12 2015
%t A035943 nmax = 60; CoefficientList[Series[Product[1 / ((1 - x^(9*k-1)) * (1 - x^(9*k-2)) * (1 - x^(9*k-3)) * (1 - x^(9*k-6)) * (1 - x^(9*k-7)) * (1 - x^(9*k-8)) ), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 12 2015 *)
%K A035943 nonn,easy
%O A035943 0,3
%A A035943 _Olivier Gérard_
%E A035943 a(0)=1 prepended by _Seiichi Manyama_, May 08 2018