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

1, 1, 2, 3, 4, 6, 8, 12, 14, 22, 24, 38, 39, 63, 62, 102, 95, 159, 144, 244, 212, 366, 309, 540, 442, 784, 626, 1125, 873, 1591, 1209, 2229, 1653, 3089, 2245, 4243, 3019, 5776, 4035, 7806, 5348, 10466, 7051, 13944, 9229, 18454, 12022, 24282, 15565, 31766, 20063

Offset: 0

Author

Emeric Deutsch, Feb 05 2006

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A100824, A100835.

Programs

Maple

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);

Mathematica

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 *)

Formula

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).