A151295 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (0, -1), (0, 1), (1, -1), (1, 0)}.

1, 2, 7, 24, 93, 364, 1490, 6178, 26163, 112001, 485272, 2120168, 9336512, 41376649, 184414880, 825963661, 3715457866, 16777860859, 76025036272, 345560464513, 1575102460028, 7197823974471, 32968875212361, 151333039522219, 696010343742969, 3206893602486167, 14800691952029228, 68415758808948051

Offset

0,2

Links

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

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. 12 (Table 5).

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[i, 1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A003041 A026558 A150402 * A150403 A150404 A150405

Adjacent sequences: A151292 A151293 A151294 * A151296 A151297 A151298

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved