A151269 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, 0), (0, -1), (0, 1), (1, -1)}.

1, 1, 3, 7, 25, 74, 281, 958, 3763, 13945, 56298, 220242, 909122, 3693263, 15531412, 64853036, 277086226, 1181341989, 5116502135, 22172843919, 97169314616, 426672066925, 1889049655130, 8385552808849, 37459538453187, 167815505507461, 755568968244344, 3411583755511270, 15467246721293668

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + 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: A148730 A148731 A148732 * A130463 A148733 A148734

Adjacent sequences: A151266 A151267 A151268 * A151270 A151271 A151272

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved