OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..800
Wikipedia, Motzkin number
MAPLE
b:= proc(x, y, t) option remember; `if`(y>x or y<0, 0,
`if`(x=0, 1, b(x-1, y-1, false) *`if`(t, x/y, 1)
+b(x-1, y, false)+b(x-1, y+1, true)))
end:
a:= n-> b(n, 0, false):
seq(a(n), n=0..30);
MATHEMATICA
b[x_, y_, t_] := b[x, y, t] = If[y>x || y<0, 0, If[x == 0, 1, b[x-1, y-1, False]*If[t, x/y, 1] + b[x-1, y, False] + b[x-1, y+1, True]]];
a[n_] := b[n, 0, False];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 10 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 25 2015
STATUS
approved