A286427 Total number of nodes summed over all lattice paths from (0,0) to (n,0) that do not go below the x-axis or above the diagonal x=y and consist of steps U=(1,1), D=(1,-1) and S=(0,1).

1, 0, 3, 5, 24, 78, 325, 1272, 5373, 22572, 97762, 425716, 1882062, 8375064, 37601643, 169773435, 771096972, 3518065767, 16119884297, 74125225732, 341970676466, 1582133854847, 7338641255894, 34117910537671, 158946919835352, 741884929970516, 3468677541274922

Offset: 0

Author

Alois P. Heinz, May 14 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A198324.

Programs

Maple

b:= proc(x, y) option remember; `if`(y<0 or y>x, 0, `if`(x=0, [1$2],
      (p-> p+[0, p[1]])(b(x, y-1)+b(x-1, y-1)+b(x-1, y+1))))
    end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=0..30);

Formula

a(n) ~ c * 2^n * (1 + sqrt(2))^n / sqrt(n), where c = 0.0205249406642810706349830917137505197586781430984... - Vaclav Kotesovec, Sep 11 2021