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A147783
Number of partitions of n into parts divisible by 2 or 5.
6
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
0,5
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
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.
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
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander E. Holroyd (holroyd at math.ubc.ca)
STATUS
approved