A147783 Number of partitions of n into parts divisible by 2 or 5.

1, 0, 1, 0, 2, 1, 3, 1, 5, 2, 8, 3, 12, 5, 17, 9, 25, 13, 35, 19, 51, 28, 69, 40, 96, 59, 129, 81, 175, 113, 236, 154, 313, 210, 412, 286, 542, 381, 705, 506, 921, 668, 1185, 875, 1525, 1148, 1948, 1485, 2485, 1918, 3157, 2462, 3990, 3150

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 or 3.

Also number of partitions of n with no part appearing 1 or 3 times.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• G. E. Andrews, A Generalization of a Partition Theorem of MacMahon, J. Combin. Theory, 3 (1967) 100-101.
• 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, A147784, A147785, A147786, A147787.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Product[(1 + x^(5*k))/(1 - x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 23 2015 *)

Formula

G.f.: Product_{k>=1} (1-x^(10k))/(1-x^(2k))/(1-x^(5k)).

a(n) ~ exp(sqrt(2*n/5)*Pi)/(4*sqrt(5)*n). - Vaclav Kotesovec, Sep 23 2015