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)}.

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

Offset

0,2

Links

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

Alin Bostan and Manuel Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008.

Mireille Bousquet-Mélou and Marni Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008.

Marni Mishna and Juan Pulido, On the small-step quarter plane lattice walks with a non D-finite univariate generating function, arXiv:2605.16688 [math.CO], 2026. See p. 13 (Table 5).

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: A026160 A025187 A373277 * A277923 A076279 A056369

Adjacent sequences: A151325 A151326 A151327 * A151329 A151330 A151331

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved