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.

A035430 Number of partitions of n into parts 7k+1 or 7k+6.

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%I A035430 #21 Mar 22 2017 10:33:22
%S A035430 1,1,1,1,1,1,2,2,3,3,3,3,4,5,6,7,8,8,9,10,12,14,16,17,19,20,23,26,30,
%T A035430 33,37,39,43,47,53,59,66,71,77,83,92,101,113,123,134,144,156,169,187,
%U A035430 204,223,240,259,278,303,329,360,389,420,449,485,522,567,613,663,710,763
%N A035430 Number of partitions of n into parts 7k+1 or 7k+6.
%C A035430 Convolution of A109708 and A109703. - _Vaclav Kotesovec_, Jan 21 2017
%H A035430 Vaclav Kotesovec, <a href="/A035430/b035430.txt">Table of n, a(n) for n = 0..10000</a>
%F A035430 a(n) ~ exp(2*Pi*sqrt(n/21)) / (4 * 21^(1/4) * sin(Pi/7) * n^(3/4)) * (1 - (3*sqrt(21)/(16*Pi) + 13*Pi/(84*sqrt(21))) / sqrt(n)). - _Vaclav Kotesovec_, Aug 26 2015, extended Jan 24 2017
%F A035430 a(n) = (1/n)*Sum_{k=1..n} A284151(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 21 2017
%t A035430 nmax = 100; CoefficientList[Series[Product[1/((1 - x^(7k+1))*(1 - x^(7k+6))), {k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 26 2015 *)
%Y A035430 Cf. A284151.
%K A035430 nonn
%O A035430 0,7
%A A035430 _Olivier Gérard_
%E A035430 Prepended a(0)=1 from _Vaclav Kotesovec_, Jan 23 2017