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A151267 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), (1, 1)} 0
1, 1, 3, 7, 21, 55, 165, 457, 1371, 3909, 11727, 33993, 101979, 298629, 895887, 2640931, 7922793, 23460851, 70382553, 209078319, 627234957, 1867531435, 5602594305, 16709292259, 50127876777, 149690954499, 449072863497, 1342297451651, 4026892354953, 12045410486339, 36136231459017, 108154061971965 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

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, -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: A161707 A192068 A318395 * A319558 A307251 A320803

Adjacent sequences:  A151264 A151265 A151266 * A151268 A151269 A151270

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified June 6 14:04 EDT 2020. Contains 334827 sequences. (Running on oeis4.)