OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
FORMULA
a(n) ~ c * d^n / sqrt(n), where d = 5.134082940807122222912767966569622... and c = 0.198313337349936555418443931967... - Vaclav Kotesovec, Apr 01 2014
MAPLE
b:= proc(x, y, k) option remember;
`if`(y<0 or y>x or k<0 or k>x^2/2-(y-x)^2/4, 0,
`if`(x=0, 1, b(x-1, y-1, k-y+1/2) +b(x-1, y+1, k-y-1/2)))
end:
a:= n-> b(4*n, 0, 4*n):
seq(a(n), n=0..30);
MATHEMATICA
b[x_, y_, k_] := b[x, y, k] = If[y<0 || y>x || k<0 || k>x^2/2-(y-x)^2/4, 0, If[x==0, 1, b[x-1, y-1, k-y+1/2] + b[x-1, y+1, k-y-1/2]]];
a[n_] := b[4n, 0, 4n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Apr 01 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 30 2014
STATUS
approved