OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 8.84734830841870961487278801886633962039798... is the real root of the equation 4 + 4*d - 8*d^2 - 8*d^3 + d^4 = 0 and c = 0.31736815701423989167651891084531024477617724724822148387263881713... - Vaclav Kotesovec, May 30 2017
MAPLE
b:= proc(x, y) option remember; `if`(y>x or y<0, 0,
`if`(x=0, 1, add(b(x-j, y)+b(x, y-j), j=1..4)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..35); # Alois P. Heinz, May 16 2017
MATHEMATICA
b[x_, y_] := b[x, y] = If[y > x || y < 0, 0, If[x == 0, 1, Sum[b[x - j, y] + b[x, y - j], {j, 1, 4}]]];
a[n_] := b[n, n];
a /@ Range[0, 35] (* Jean-François Alcover, Nov 11 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Werley, Dec 05 2010
STATUS
approved