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A114312 Number of partitions of n with at most 3 odd parts.

%I A114312 #8 Mar 07 2016 06:34:08
%S A114312 1,1,2,3,4,6,8,12,14,22,24,38,39,63,62,102,95,159,144,244,212,366,309,
%T A114312 540,442,784,626,1125,873,1591,1209,2229,1653,3089,2245,4243,3019,
%U A114312 5776,4035,7806,5348,10466,7051,13944,9229,18454,12022,24282,15565,31766,20063
%N A114312 Number of partitions of n with at most 3 odd parts.
%H A114312 Alois P. Heinz, <a href="/A114312/b114312.txt">Table of n, a(n) for n = 0..1000</a>
%F A114312 G.f.: (1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4)+x^3/(1-x^2)/(1-x^4)/(1-x^6))/Product(1-x^(2*i), i=1..infinity).
%e A114312 a(6) = 8 because we have 6, 51, 42, 411, 33, 321, 222 and 2211 (3111, 21111 and 111111 do not qualify).
%p A114312 G:=(1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4)+x^3/(1-x^2)/(1-x^4)/(1-x^6))/Product(1-x^(2*i), i=1..100): Gser:=series(G, x, 70): seq(coeff(Gser, x, n), n=0..60);
%t A114312 nmax = 50; CoefficientList[Series[(1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4)+x^3/(1-x^2)/(1-x^4)/(1-x^6)) * Product[1/(1-x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 07 2016 *)
%Y A114312 Cf. A100824, A100835.
%K A114312 nonn
%O A114312 0,3
%A A114312 _Emeric Deutsch_, Feb 05 2006