OFFSET
0,19
COMMENTS
Number of partitions into distinct parts 4*k+3.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
FORMULA
G.f. sum(n>=0, x^(2*n^2+n) / prod(k=1,n, 1-x^(4*k))) - Joerg Arndt, Mar 10 2011.
a(n) ~ exp(sqrt(n/3)*Pi/2) / (4*6^(1/4)*n^(3/4)) * (1 - (3*sqrt(3)/(4*Pi) + Pi/(192*sqrt(3))) / sqrt(n)). - Vaclav Kotesovec, Jan 18 2017
MATHEMATICA
nmax = 200; CoefficientList[Series[Product[(1 + x^(4*k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 18 2017 *)
nmax = 200; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 4] == 3, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly (* Vaclav Kotesovec, Jan 18 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 29 2010
STATUS
approved