A151301 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), (1, -1), (1, 1)}

1, 2, 8, 29, 124, 520, 2299, 10185, 46139, 210288, 969337, 4493757, 20975812, 98367797, 463470713, 2191776623, 10401020754, 49503229100, 236245016604, 1130119433626, 5417868668788, 26024413525094, 125230444119430, 603596991872618, 2913639052387674, 14083936989164572, 68165897301953131

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[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: A150737 A150738 A150739 * A150740 A150741 A150742

Adjacent sequences: A151298 A151299 A151300 * A151302 A151303 A151304

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved