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

0,9

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.

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

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 *)

Crossrefs

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

Sequence in context: A324642 A371740 A326757 * A247288 A135221 A318686

Adjacent sequences: A147784 A147785 A147786 * A147788 A147789 A147790

Keyword

nonn

Author

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

Status

approved