OFFSET
0,3
COMMENTS
a(n) is the number of overpartitions wherein only parts that are a multiple of four may be overlined. - Alois P. Heinz, Feb 03 2025
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..5000
FORMULA
a(n) ~ sqrt(3) * exp(sqrt(3*n)*Pi/2) / (16*n).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1)+`if`(irem(i, 4)=0, 2, 1)*add(b(n-i*j, i-1), j=1..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..45); # Alois P. Heinz, Feb 03 2025
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[((1+x^(4*k))/(1-x^k)), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Apr 19 2017
STATUS
approved