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A147787 Number of partitions of n into parts divisible by 4,6 or 9. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A305736 A324642 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

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Last modified October 24 18:08 EDT 2021. Contains 348233 sequences. (Running on oeis4.)