A151256 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), (0, 1), (1, -1)}

1, 1, 2, 4, 10, 23, 61, 153, 418, 1100, 3064, 8307, 23447, 64864, 184825, 518709, 1488535, 4222233, 12183197, 34838780, 100966510, 290552075, 845040527, 2444044917, 7129099964, 20703110094, 60537979132, 176393527768, 516869732557, 1510240001769, 4433253350132, 12983932323027, 38173103248661

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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

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, 1 + j, -1 + n] + aux[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: A032171 A127713 A354076 * A205999 A208126 A370646

Adjacent sequences: A151253 A151254 A151255 * A151257 A151258 A151259

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved