OFFSET
0,4
COMMENTS
Euler transform of period 3 sequence [ 1, 0, 1, ...]. - Kevin T. Acres, Apr 28 2018
LINKS
Robert Price, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ Gamma(1/3) * exp(2*Pi*sqrt(n)/3) / (4 * sqrt(3) * Pi^(2/3) * n^(11/12)). - Vaclav Kotesovec, Aug 23 2015
EXAMPLE
1 + x + x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 5*x^6 + 7*x^7 + 8*x^8 + 11*x^9 + ...
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[1/((1 - x^(3*k))*(1 - x^(3*k-2))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 23 2015 *)
nmax = 52; kmax = nmax/3;
s = Flatten[{Range[0, kmax]*3}~Join~{Range[0, kmax]*3 + 1}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* Robert Price, Aug 02 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved