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
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.
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