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

0,3

Links

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

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).

Example

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

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 *)

Crossrefs

Cf. A100824, A100835.

Sequence in context: A101902 A236912 A215966 * A095041 A331088 A336506

Adjacent sequences: A114309 A114310 A114311 * A114313 A114314 A114315

Keyword

nonn

Author

Emeric Deutsch, Feb 05 2006

Status

approved