A151294 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), (0, 1), (1, -1), (1, 1)}

1, 2, 7, 24, 91, 339, 1316, 5064, 19876, 77655, 306653, 1207928, 4787659, 18949972, 75289153, 298902364, 1189498285, 4731773527, 18852187670, 75095222625, 299445133063, 1193945935638, 4763913059444, 19007869938607, 75878972921436, 302911103389119, 1209664171630344, 4830899882203163

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, -1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A150392 A150393 A150394 * A196470 A339785 A150395

Adjacent sequences: A151291 A151292 A151293 * A151295 A151296 A151297

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved