OFFSET
0,15
COMMENTS
Number of partitions of n into parts larger than 1 and congruent to 1 mod 3.
More generally, the ordinary generating function for the number of partitions of n into parts larger than 1 and congruent to 1 mod m (for m>0) is Product_{k>=1} 1/(1 - x^(m*k+1)).
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^(3*k+1)).
a(n) ~ Pi^(1/3) * Gamma(1/3) * exp(sqrt(2*n)*Pi/3) / (2^(13/6)*3^(3/2)*n^(7/6)). - Vaclav Kotesovec, Oct 06 2016
EXAMPLE
a(14) = 2, because we have [10, 4] and [7, 7].
MATHEMATICA
CoefficientList[Series[(1 - x)/QPochhammer[x, x^3], {x, 0, 85}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 05 2016
STATUS
approved