OFFSET
0,3
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..650
Wikipedia, Counting lattice paths
EXAMPLE
a(3) = (1+1+1) + (1+2) + 2 + (2+2) + 3 = 15:
/\
/\ /\ /\/\ / \
/\/\/\ /\/ \ / \/\ / \ / \ .
MAPLE
b:= proc(x, y, t, h) option remember; `if`(x=0, [1, 0], `if`(y>0,
(p-> p+[0, `if`(t=1, p[1]*h, 0)])(b(x-1, y-1, 0, h)), 0)+
`if`(y<x-1, b(x-1, y+1, `if`(y+1>=h, 1, 0), max(h, y+1)), 0))
end:
a:= n-> b(2*n, 0$3)[2]:
seq(a(n), n=0..32);
MATHEMATICA
b[x_, y_, t_, h_] := b[x, y, t, h] = If[x == 0, {1, 0}, If[y > 0,
Function[p, p + {0, If[t == 1, p[[1]]*h, 0]}][b[x-1, y-1, 0, h]], 0] +
If[y < x-1, b[x-1, y+1, If[y+1 >= h, 1, 0], Max[h, y+1]], 0]];
a[n_] := b[2*n, 0, 0, 0][[2]];
Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Jun 04 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 09 2021
STATUS
approved