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.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

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