OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1665
Wikipedia, Counting lattice paths
Wikipedia, Motzkin number
MAPLE
b:= proc(x, y) option remember; `if`(x=0, [1, 0], add(
(p-> p+[0, p[1]*(y+j/2)])(b(x-1, y+j)),
j=-min(1, y)..min(max(1, y), x-y-1)))
end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=0..29);
MATHEMATICA
b[x_, y_] := b[x, y] = If[x == 0, {1, 0}, Sum[
Function[p, p + {0, p[[1]]*(y + j/2)}][b[x - 1, y + j]],
{j, -Min[1, y], Min[Max[1, y], x - y - 1]}]];
a[n_] := b[n, 0][[2]];
a /@ Range[0, 29] (* Jean-François Alcover, Apr 05 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 07 2020
STATUS
approved