A151280 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (0, 1), (1, 0)}

1, 2, 5, 15, 47, 150, 495, 1672, 5698, 19636, 68470, 240342, 848258, 3012899, 10753669, 38519879, 138501666, 499728140, 1807946861, 6557502077, 23843549009, 86880613032, 317170036587, 1160001218633, 4249640363945, 15591664759190, 57285869534363, 210757677563396, 776332308628500, 2862899274870651

Offset

0,2

Links

Table of n, a(n) for n=0..29.

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

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

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[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A308274 A058495 A287275 * A149914 A071735 A148363

Adjacent sequences: A151277 A151278 A151279 * A151281 A151282 A151283

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved