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

0,2

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.

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

Example

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].

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 *)

Prog

(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

Crossrefs

Cf. A098151.

Sequence in context: A008609 A264392 A100823 * A333148 A343661 A342229

Adjacent sequences: A102343 A102344 A102345 * A102347 A102348 A102349

Keyword

nonn

Author

Noureddine Chair, Feb 21 2005

Extensions

Corrected by Vladeta Jovovic, Feb 21 2005

Offset and example corrected by Vaclav Kotesovec, Sep 01 2015

Status

approved