OFFSET
0,2
COMMENTS
Partial sums of A003105.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..2000
Eric Weisstein's World of Mathematics, Schur's Partition Theorem
FORMULA
G.f.: (1/(1 - x))*Product_{k>=0} 1/((1 - x^(6*k+1))*(1 - x^(6*k+5))).
G.f.: (1/(1 - x))*Product_{k>=0} 1/(1 - x^k + x^(2*k)).
a(n) ~ exp(sqrt(2*n)*Pi/3) * sqrt(3) / (Pi * 2^(3/4) * n^(1/4)). - Vaclav Kotesovec, May 19 2018
MATHEMATICA
nmax = 57; CoefficientList[Series[1/(1 - x) Product[(1 + x^k)/(1 + x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 57; CoefficientList[Series[1/(1 - x) Product[1/((1 - x^(6 k + 1)) (1 - x^(6 k + 5))), {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 57; CoefficientList[Series[1/(1 - x) Product[1/(1 - x^k + x^(2 k)), {k, 0, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 15 2018
STATUS
approved