A151273 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), (1, -1), (1, 1)}.

1, 1, 4, 11, 42, 130, 506, 1701, 6678, 23348, 92162, 330718, 1310042, 4785834, 19002354, 70329169, 279708134, 1045513784, 4163154786, 15682361864, 62502107274, 236910288210, 944854095762, 3599694071586, 14364065086506, 54956626517442, 219388412771714, 842388119494786, 3363960168087706

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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. 14 (Table 7).

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[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: A032265 A320155 A260320 * A149271 A149272 A149273

Adjacent sequences: A151270 A151271 A151272 * A151274 A151275 A151276

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved