OFFSET
0,4
LINKS
Cristina Ballantine and Mircea Merca, 4-Regular partitions and the pod function, arXiv:2111.10702 [math.CO], 2021.
FORMULA
EXAMPLE
a(6) = 4 because we have [6], [3, 2, 1], [2, 2, 2] and [2, 1, 1, 1, 1].
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<1, 0,
b(n, i-1, t)+`if`(irem(i, 4)=0, 0, b(n-i, min(n-i, i), 1-t))))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..55); # Alois P. Heinz, Dec 03 2020
MATHEMATICA
nmax = 53; CoefficientList[Series[(1/2) (Product[(1 - x^(4 k))/(1 - x^k), {k, 1, nmax}] - Product[(1 + x^(4 k))/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 03 2020
STATUS
approved