A151298 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), (1, -1), (1, 0)}

1, 2, 7, 28, 118, 531, 2468, 11803, 57684, 286757, 1446170, 7379881, 38043130, 197822526, 1036473665, 5466733758, 29003678329, 154689197699, 828926263122, 4460905720669, 24099684585681, 130657255240514, 710658902564016, 3876874286092771, 21207804910818281, 116309469589961213, 639383247986188829

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + n] + aux[-1 + 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: A090317 A150650 A150651 * A161944 A150652 A130655

Adjacent sequences: A151295 A151296 A151297 * A151299 A151300 A151301

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved