A151303 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), (1, -1), (1, 0), (1, 1)}.

1, 2, 8, 30, 122, 508, 2163, 9336, 40804, 179887, 799120, 3571698, 16048114, 72428799, 328167457, 1491978164, 6803716892, 31110321096, 142600055057, 655074921487, 3015313208782, 13904953770666, 64229950295692, 297152727581176, 1376720785809034, 6386921652633456, 29667247964299526, 137964512850757605

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, -1 + j, -1 + n] + aux[-1 + i, j, -1 + n] + aux[-1 + 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: A150759 A150760 A230588 * A150761 A373176 A150762

Adjacent sequences: A151300 A151301 A151302 * A151304 A151305 A151306

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved