%I #8 Mar 07 2016 06:34:08

%S 1,1,2,3,4,6,8,12,14,22,24,38,39,63,62,102,95,159,144,244,212,366,309,

%T 540,442,784,626,1125,873,1591,1209,2229,1653,3089,2245,4243,3019,

%U 5776,4035,7806,5348,10466,7051,13944,9229,18454,12022,24282,15565,31766,20063

%N Number of partitions of n with at most 3 odd parts.

%H Alois P. Heinz, <a href="/A114312/b114312.txt">Table of n, a(n) for n = 0..1000</a>

%F 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 a(6) = 8 because we have 6, 51, 42, 411, 33, 321, 222 and 2211 (3111, 21111 and 111111 do not qualify).

%p 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 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 Cf. A100824, A100835.

%K nonn

%O 0,3

%A _Emeric Deutsch_, Feb 05 2006