OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ exp(Pi*sqrt(n/3)) / (8 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Oct 09 2018
MAPLE
h:= proc(n) option remember; `if`(n=0, 0, irem(n, 2, 'q')+h(q)) end:
b:= proc(n, i, t) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, t,
b(n, i-1, t)+b(n-i, min(n-i, i-1), irem(t+h(i), 2))))
end:
a:= n-> b(n$2, 1):
seq(a(n), n=0..100);
MATHEMATICA
h[n_] := h[n] = If[n == 0, 0, Mod[n, 2] + h[Quotient[n, 2]]];
b[n_, i_, t_] := b[n, i, t] = If[i(i+1)/2 < n, 0, If[n == 0, t, b[n, i - 1, t] + b[n - i, Min[n - i, i - 1], Mod[t + h[i], 2]]]];
a[n_] := b[n, n, 1];
a /@ Range[0, 100](* Jean-François Alcover, Dec 12 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 24 2018
STATUS
approved