A109705 - OEIS

%I #16 Mar 28 2017 14:48:19

%S 1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,1,1,1,2,1,1,2,2,1,2,3,1,2,4,2,2,4,

%T 4,2,4,5,3,4,6,5,4,6,7,5,6,8,8,6,9,11,7,9,13,10,9,14,14,10,15,17,14,

%U 15,19,19,16,20,24,20,21,27,27,22,29,33,27,30,38,35,32,41,44,37,43,51,47,45

%N Number of partitions of n into parts each equal to 3 mod 7.

%H Vaclav Kotesovec, <a href="/A109705/b109705.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: 1/product(1-x^(3+7j), j=0..infinity). - _Emeric Deutsch_, Apr 14 2006

%F a(n) ~ Gamma(3/7) * exp(Pi*sqrt(2*n/21)) / (2^(12/7) * 3^(3/14) * 7^(2/7) * Pi^(4/7) * n^(5/7)) * (1 + (23*Pi/(168*sqrt(42)) - 15*sqrt(3/14)/(7*Pi)) / sqrt(n)). - _Vaclav Kotesovec_, Feb 27 2015, extended Jan 24 2017

%F a(n) = (1/n)*Sum_{k=1..n} A284444(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 28 2017

%e a(20)=2 because we have 20=17+3=10+10.

%p g:=1/product(1-x^(3+7*j),j=0..20): gser:=series(g,x=0,90): seq(coeff(gser,x,n),n=0..87); # _Emeric Deutsch_, Apr 14 2006

%t nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+3)),{k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 27 2015 *)

%K nonn

%O 0,21

%A _Erich Friedman_, Aug 07 2005

%E Changed offset to 0 and added a(0)=1 by _Vaclav Kotesovec_, Feb 27 2015