A151280 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), (0, 1), (1, 0)}.

1, 2, 5, 15, 47, 150, 495, 1672, 5698, 19636, 68470, 240342, 848258, 3012899, 10753669, 38519879, 138501666, 499728140, 1807946861, 6557502077, 23843549009, 86880613032, 317170036587, 1160001218633, 4249640363945, 15591664759190, 57285869534363, 210757677563396, 776332308628500, 2862899274870651

Offset

0,2

Links

Table of n, a(n) for n=0..29.

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[i, -1 + j, -1 + n] + aux[1 + i, -1 + 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: A308274 A058495 A287275 * A149914 A071735 A391035

Adjacent sequences: A151277 A151278 A151279 * A151281 A151282 A151283

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved