OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..400
FORMULA
a(n) ~ 2^(24*n + 4) / (3^(3*n + 1/2) * 5^(5*n + 7/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 14 2017
MAPLE
b:= proc(x, y, k) option remember;
`if`(x=0, 1, `if`(y>0, b(x-1, y-1, k), 0)+
`if`(y < min(x-1, k), b(x-1, y+1, k), 0))
end:
a:= n-> `if`(n=0, 1, b(8*n, 0, n)-b(8*n, 0, n-1)):
seq(a(n), n=0..20);
MATHEMATICA
b[x_, y_, k_]:=b[x, y, k]=If[x==0, 1, If[y>0, b[x - 1, y - 1, k], 0] + If[y<Min[x - 1, k], b[x - 1, y + 1, k], 0]]; a[n_]:=a[n]=If[n==0, 1, b[8n, 0, n] - b[8n, 0, n - 1]]; Table[a[n], {n, 0, 20}] (* Indranil Ghosh, Jul 08 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 06 2017
STATUS
approved