A151322 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), (1,0), (1,1)}.

1, 3, 14, 65, 330, 1683, 8874, 47088, 253802, 1375939, 7524651, 41346061, 228447273, 1267005772, 7054307476, 39394861448, 220641191059, 1238773724011, 6970910527593, 39305772011050, 222039381179593, 1256404002028860, 7120347445063067, 40409910873522737, 229639109317630051, 1306567259328079561

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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.

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, 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: A026592 A034275 A240008 * A373450 A351068 A345683

Adjacent sequences: A151319 A151320 A151321 * A151323 A151324 A151325

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved