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%I #39 Jul 17 2019 17:13:36
%S 1,1,1,1,1,1,1,2,2,2,2,2,2,3,4,4,4,4,4,5,6,7,7,7,7,8,10,11,12,12,12,
%T 13,15,17,18,19,19,20,23,26,28,29,30,31,34,38,41,43,44,46,50,55,60,63,
%U 65,67,72,79,85,90,93,96,102,111,120,127,132,136,143,154,166,176,183,189,198
%N Number of partitions of n into parts each equal to 1 mod 6.
%C Euler transform of period 6 sequence [ 1, 0, 0, 0, 0, 0, ...]. - _Kevin T. Acres_, Apr 28 2018
%H Vaclav Kotesovec, <a href="/A109701/b109701.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: 1/Product_{j >= 0} (1-x^(1+6j)). - _Emeric Deutsch_, Apr 14 2006
%F a(n) ~ Gamma(1/6) * exp(Pi*sqrt(n)/3) / (4 * sqrt(3) * Pi^(5/6) * n^(7/12)) * (1 - (7/(24*Pi) + Pi/144) / sqrt(n)). - _Vaclav Kotesovec_, Feb 27 2015, extended Jan 24 2017
%F a(n) = (1/n)*Sum_{k=1..n} A284098(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 20 2017
%F G.f.: Sum_{k>=0} x^k / Product_{j=1..k} (1 - x^(6*j)). - _Ilya Gutkovskiy_, Jul 17 2019
%e a(10)=2 since 10 = 7+1+1+1 = 1+1+1+1+1+1+1+1+1+1
%p g:=1/product(1-x^(1+6*j),j=0..20): gser:=series(g,x=0,77): seq(coeff(gser,x,n),n=0..74); # _Emeric Deutsch_, Apr 14 2006
%t nmax=100; CoefficientList[Series[Product[1/(1-x^(6*k+1)),{k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 27 2015 *)
%Y Cf. A284098.
%Y Cf. similar sequences of number of partitions of n into parts congruent to 1 mod m: A000009 (m=2), A035382 (m=3), A035451 (m=4), A109697 (m=5), this sequence (m=6), A109703 (m=7), A277090 (m=8).
%K nonn
%O 0,8
%A _Erich Friedman_, Aug 07 2005
%E Changed offset to 0 and added a(0)=1 by _Vaclav Kotesovec_, Feb 27 2015
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