A151319 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (0, -1), (0, 1), (1, 0), (1, 1)}.

1, 3, 13, 57, 263, 1233, 5869, 28201, 136471, 664031, 3244373, 15904999, 78180131, 385141745, 1900808447, 9395586359, 46502309921, 230413447773, 1142763706389, 5672369968137, 28176421469243, 140049400473211, 696494762630355, 3465512981413485, 17250679866579039, 85903957507564797

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[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: A115968 A256939 A005827 * A151222 A349299 A151223

Adjacent sequences: A151316 A151317 A151318 * A151320 A151321 A151322

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved