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.
%I A109702 #36 Mar 08 2022 15:37:11
%S A109702 1,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,1,1,0,0,1,1,2,1,0,1,1,2,2,1,1,1,2,3,
%T A109702 3,2,1,2,3,4,4,2,2,3,5,6,5,3,3,5,7,8,6,4,5,8,10,10,8,6,8,11,13,13,10,
%U A109702 9,12,15,18,17,14,13,16,21,23,22,18,18,23,28,31,28,24,25,31,38,39,36,32,34
%N A109702 Number of partitions of n into parts each equal to 5 mod 6.
%H A109702 Vaclav Kotesovec, <a href="/A109702/b109702.txt">Table of n, a(n) for n = 0..10000</a>
%F A109702 G.f.: 1/product(1-x^(5+6j),j=0..infinity). - _Emeric Deutsch_, Apr 14 2006
%F A109702 a(n) ~ Gamma(5/6) * exp(Pi*sqrt(n)/3) / (4 * sqrt(3) * Pi^(1/6) * n^(11/12)) * (1 - (55/(24*Pi) + Pi/144) / sqrt(n)). - _Vaclav Kotesovec_, Feb 27 2015, extended Jan 24 2017
%F A109702 a(n) = (1/n)*Sum_{k=1..n} A284104(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 20 2017
%F A109702 Euler transform of period 6 sequence [ 0, 0, 0, 0, 1, 0, ...]. - _Kevin T. Acres_, Apr 28 2018
%e A109702 a(40)=4 since 40 = 35+5 = 29+11 = 23+17 = 5+5+5+5+5+5+5+5.
%p A109702 g:=1/product(1-x^(5+6*j),j=0..20): gser:=series(g,x=0,92): seq(coeff(gser,x,n),n=0..89); # _Emeric Deutsch_, Apr 14 2006
%t A109702 nmax=100; CoefficientList[Series[Product[1/(1-x^(6*k+5)),{k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 27 2015 *)
%t A109702 Table[Count[IntegerPartitions[n],_?(Union[Mod[#,6]]=={5}&)],{n,0,90}] (* _Harvey P. Dale_, Mar 08 2022 *)
%Y A109702 Cf. A284104.
%Y A109702 Cf. similar sequences of number of partitions of n into parts congruent to m-1 mod m: A000009 (m=2), A035386 (m=3), A035462 (m=4), A109700 (m=5), this sequence (m=6), A109708 (m=7).
%K A109702 nonn
%O A109702 0,23
%A A109702 _Erich Friedman_, Aug 07 2005
%E A109702 Changed offset to 0 and added a(0)=1 by _Vaclav Kotesovec_, Feb 27 2015