A151508 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, -1), (1, -1), (1, 0)}.

1, 0, 2, 1, 12, 13, 106, 184, 1167, 2749, 14976, 43184, 214494, 709375, 3334182, 12111401, 55172493, 213825895, 958512287, 3886970215, 17308095926, 72488219249, 322457272822, 1382555862308, 6164246110975, 26897094736460, 120411455688784, 532534766552745, 2395778998202593, 10709328780143584

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..440

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

Maple

b:= proc(n, x, y) option remember; `if` (n<0 or x<0 or y<0 or n<x, 0, `if` (n=0, `if` (x=0, 1, 0), add (b(n-1, x+d[1], y+d[2]), d=[[-1, -1], [-1, 0], [-1, 1], [0, -1], [1, -1], [1, 0]]))) end: a:= n-> b(n, 0, 0):
seq (a(n), n=0..30);  # Alois P. Heinz, Jul 02 2011

Mathematica

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A199930 A278330 A048854 * A164826 A055392 A045873

Adjacent sequences: A151505 A151506 A151507 * A151509 A151510 A151511

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved