A151276 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, 0), (0, -1), (1, -1), (1, 1)}.

1, 1, 5, 17, 69, 273, 1181, 5049, 22277, 98801, 445357, 2019337, 9240325, 42516417, 196833789, 915399225, 4276244117, 20050107057, 94335358413, 445185708105, 2106762523813, 9994758390849, 47525328431357, 226456780880985, 1081142185822101, 5170719824783825, 24770430475804429, 118844354630579049

Offset

0,3

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. 6 (Table 3).

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

Crossrefs

Sequence in context: A149697 A149698 A149699 * A272743 A149700 A149701

Adjacent sequences: A151273 A151274 A151275 * A151277 A151278 A151279

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved