OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1666
Wikipedia, Counting lattice paths
FORMULA
a(n) ~ c * 4^n / sqrt(n), where c = 0.028711801689489498782112731663771630297082311282971968906589032765122715... - Vaclav Kotesovec, Oct 24 2020
MAPLE
b:= proc(x, y) option remember; `if`(x=0, [1$2],
add(add((p-> p+[0, p[1]])(b(x-h, y-v)), h=1..
min(x-y+v, max(1, y-v))), v=-1..min(y, 1)))
end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=0..30);
MATHEMATICA
b[x_, y_] := b[x, y] = If[x == 0, {1, 1},
Sum[Sum[Function[p, p + {0, p[[1]]}][b[x - h, y - v]], {h, 1,
Min[x - y + v, Max[1, y - v]]}], {v, -1, Min[y, 1]}]];
a[n_] := b[n, 0][[2]];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 22 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 12 2020
STATUS
approved