A151325 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, -1), (1, 0), (1, 1)}.

1, 3, 14, 69, 364, 1964, 10862, 60849, 344914, 1970654, 11336210, 65550856, 380715692, 2219101122, 12974182136, 76050379457, 446774956662, 2629721680448, 15504560993606, 91547835411002, 541254436678564, 3203730923576886, 18982695363209084, 112579789273032820, 668226265440813776

Offset

0,2

Links

Table of n, a(n) for n=0..24.

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. 15 (Table 8).

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, -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: A199314 A360144 A190725 * A020065 A028938 A038213

Adjacent sequences: A151322 A151323 A151324 * A151326 A151327 A151328

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved