A151274 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), (1, -1), (1, 1)}

1, 1, 5, 13, 51, 179, 685, 2609, 10269, 40435, 162355, 654197, 2663021, 10896113, 44862303, 185524733, 770809891, 3213995231, 13449327811, 56449627333, 237606240991, 1002649516511, 4240932519555, 17976119289559, 76346766385593, 324842947451253, 1384493839712331, 5910024485652133

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[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: A146657 A243304 A238508 * A149538 A149539 A007231

Adjacent sequences: A151271 A151272 A151273 * A151275 A151276 A151277

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved