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.

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. 7 (Theorem 7, Table 4).

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