A151263 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), (0, -1), (0, 1), (1, -1)}.

1, 1, 3, 6, 20, 52, 175, 526, 1793, 5841, 20253, 69270, 244522, 862772, 3097566, 11167024, 40692846, 149065293, 550140081, 2040710835, 7613008077, 28530887220, 107416078626, 406033088229, 1540733604031, 5866919041227, 22414534958855, 85896861535871, 330124332489755, 1272178553484815, 4914991500737809

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[i, -1 + j, -1 + n] + aux[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: A148578 A182299 A148579 * A148580 A148581 A148582

Adjacent sequences: A151260 A151261 A151262 * A151264 A151265 A151266

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved