A102346 Number of partitions of 2n in which odd parts and multiples of 3 and 5 occur with even multiplicities. There is no restriction on the other even parts.

1, 2, 4, 7, 12, 19, 30, 46, 69, 101, 146, 208, 293, 408, 563, 769, 1042, 1401, 1871, 2482, 3273, 4291, 5596, 7261, 9378, 12057, 15437, 19684, 25005, 31648, 39919, 50184, 62890, 78573, 97883, 121597, 150653, 186169, 229487, 282204, 346230, 423831, 517706

Offset: 0

Author

Noureddine Chair, Feb 21 2005

Keywords

• nonn

Examples

			a(5) = 19: [8,2], [8,1,1], [5,5], [4,4,2], [4,4,1,1], [4,2,2,2], [4,2,2,1,1], [4,2,1,1,1,1], [4,3,3], [3,3,2,2], [3,3,2,1,1], [3,3,1,1,1,1], [4,1,1,1,1,1,1], [2,2,2,2,2], [2,2,2,2,1,1], [2,2,2,1,1,1,1], [2,2,1,1,1,1,1,1], [2,1,1,1,1,1,1,1,1], [1,1,1,1,1,1,1,1,1,1].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Noureddine Chair, Partition Identities From Partial Supersymmetry, arXiv:hep-th/0409011v1, 2004.

Crossrefs

Cf. A098151.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1+x^k)*(1+x^(15*k))/((1-x^k)*(1+x^(3*k))*(1+x^(5*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 01 2015 *)

PARI

q='q+O('q^33); E(k)=eta(q^k);
Vec( (E(2)*E(3)*E(5)*E(30)) / (E(1)^2*E(6)*E(10)*E(15)) ) \\ Joerg Arndt, Sep 01 2015

Formula

G.f.: Product((1+x^k)*(1+x^(15*k))/((1-x^k)*(1+x^(3*k))*(1+x^(5*k))), k>=1).

a(n) ~ exp(Pi*sqrt(38*n/5)/3) * sqrt(19) / (12*sqrt(5)*n). - Vaclav Kotesovec, Sep 01 2015

G.f.: (E(2)*E(3)*E(5)*E(30)) / (E(1)^2*E(6)*E(10)*E(15)) where E(k) = prod(n>=1, 1-q^k ). - Joerg Arndt, Sep 01 2015

Extensions

Corrected by Vladeta Jovovic, Feb 21 2005

Offset and example corrected by Vaclav Kotesovec, Sep 01 2015