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A151328 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, 0), (0, -1), (0, 1), (1, -1), (1, 0), (1, 1)} 0
1, 3, 16, 84, 484, 2843, 17193, 105553, 657177, 4133074, 26217040, 167455754, 1075896508, 6947158172, 45052303360, 293263303568, 1915285138362, 12545294612032, 82387919461119, 542332725044387, 3577577193573774, 23645483214136620, 156556003183195069, 1038219939150227788, 6895261278418168211 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

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

CROSSREFS

Sequence in context: A026131 A026160 A025187 * A277923 A076279 A056369

Adjacent sequences:  A151325 A151326 A151327 * A151329 A151330 A151331

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 22 14:23 EST 2021. Contains 340362 sequences. (Running on oeis4.)