A175883 Number of lattice paths from (0,0) to (n,n) using steps S={(k,0),(0,k)|0<k<=3} which never go above the line y=x.

1, 1, 5, 29, 170, 1093, 7346, 50957, 362476, 2629150, 19371533, 144585146, 1090886362, 8306621114, 63752890716, 492671044866, 3830272606911, 29937476853483, 235104315621495, 1854181694878573, 14679397763545597, 116619744085592959, 929412502842262520

Offset

0,3

Links

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

Example

a(3)=29 because we can reach (3,3) in the following ways:
by getting to (3,2) in 17 ways and then taking step (0,1), or
by getting to (3,1) in 8 ways and then taking step (0,2), or
by getting to (3,0) in 4 ways and then taking step (0,3).

Maple

b:= proc(x, y) option remember; `if`(y>x or y<0, 0,
      `if`(x=0, 1, add(b(x-j, y)+b(x, y-j), j=1..3)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..35);  # Alois P. Heinz, May 16 2017

Mathematica

b[x_, y_] := b[x, y] = If[y > x || y < 0, 0, If[x == 0, 1, Sum[b[x - j, y] + b[x, y - j], {j, 1, 3}]]];
a[n_] := b[n, n];
a /@ Range[0, 35] (* Jean-François Alcover, Nov 11 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000108, A122951.

Sequence in context: A227206 A001653 A141814 * A122370 A088349 A272802

Adjacent sequences: A175880 A175881 A175882 * A175884 A175885 A175886

Keyword

nonn

Author

Eric Werley, Dec 05 2010

Status

approved