A147786 Number of partitions of n into parts divisible by 4 or 5.

1, 0, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 3, 2, 2, 3, 5, 3, 4, 3, 11, 5, 6, 6, 15, 13, 10, 9, 23, 17, 23, 15, 34, 27, 31, 33, 50, 40, 48, 45, 86, 60, 71, 69, 116, 106, 105, 102, 169, 144, 176, 150, 237, 211, 240, 248, 335, 299, 347, 338, 506, 425, 487, 487, 681

Offset

0,9

Comments

Also number of partitions of n with no part and no difference between two parts equal to 1,2,3,6,7 or 11.

Also number of partitions of n with no part appearing 1,2,3,6,7 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^(20k))/(1-x^(4k))/(1-x^(5k)).

a(n) ~ exp(2*Pi*sqrt(n/15))/(2*sqrt(30)*n). - Vaclav Kotesovec, Sep 23 2015

Mathematica

nmax = 60; CoefficientList[Series[Product[(1 + x^(5*k))*(1 + x^(10*k))/(1 - x^(4*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 23 2015 *)

Crossrefs

Cf. A007690, A147783, A147784, A147785, A147787.

Sequence in context: A238735 A356006 A258120 * A275019 A337835 A119387

Adjacent sequences: A147783 A147784 A147785 * A147787 A147788 A147789

Keyword

nonn

Author

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

Status

approved