A151364 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, -1), (0, 1), (1, 0)}.

1, 0, 2, 2, 10, 26, 86, 312, 1022, 3978, 14098, 55214, 209256, 825384, 3259848, 13047190, 52796942, 214867958, 883609140, 3650644490, 15200444924, 63591578852, 267560620976, 1130884163454, 4801237259556, 20467269154810, 87575978537798, 376056564410360, 1620031193788260, 7000548312843696

Offset

0,3

Links

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

A. Bostan, K. Raschel, B. Salvy, Non-D-finite excursions in the quarter plane, J. Comb. Theory A 121 (2014) 45-63, Table 1 Tag 24, Tag 38.

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

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

Crossrefs

Sequence in context: A213338 A309753 A102345 * A200949 A001885 A300641

Adjacent sequences: A151361 A151362 A151363 * A151365 A151366 A151367

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved