A147787 Number of partitions of n into parts divisible by 4,6 or 9.

1, 0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 4, 1, 2, 1, 6, 2, 6, 1, 9, 4, 8, 2, 17, 6, 13, 7, 23, 9, 24, 9, 35, 18, 34, 15, 58, 24, 51, 28, 80, 37, 84, 40, 115, 64, 116, 60, 175, 88, 168, 101, 239, 128, 258, 139, 335, 199, 352, 203, 487, 273, 494, 315, 656, 386, 714

Offset: 0

Author

Alexander E. Holroyd (holroyd at math.ubc.ca)

Keywords

• nonn

Comments

Also number of partitions of n with no part and no difference between two parts equal to 1,2,3,5,7 or 11.

Also number of partitions of n with no part appearing 1,2,3,5,7 or 11 times.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• A. E. Holroyd, Partition Identities and the Coin Exchange Problem, arXiv:0706.2282 [math.CO], 2007.
• A. E. Holroyd, Partition Identities and the Coin Exchange Problem, J. Combin. Theory Ser. A, 115 (2008) 1096-1101.

Crossrefs

Cf. A007690, A147783, A147784, A147785, A147786.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Product[(1 + x^(9*k))*(1 + x^(6*k))/(1 - x^(4*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 23 2015 *)

Formula

G.f.: Product_{k>=1} (1-x^(12k))(1-x^(18k))/(1-x^(4k))/(1-x^(6k))/(1-x^(9k)).

a(n) ~ sqrt(7/6)*exp(sqrt(7*n/3)*Pi/3)/(12*n). - Vaclav Kotesovec, Sep 23 2015