A151306 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, 1), (-1, 0), (1, 0), (1, 1)}

1, 2, 9, 29, 139, 511, 2498, 9781, 48238, 196055, 971491, 4047652, 20113296, 85304735, 424646194, 1825369912, 9097470592, 39520352083, 197127302029, 863661309954, 4310448703844, 19018425833689, 94959280164706, 421465934703502, 2105044748278047, 9390456216012559, 46912406079449786, 210193393267663019

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, j, -1 + n] + aux[1 + 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: A268568 A150902 A150903 * A150904 A122675 A042357

Adjacent sequences: A151303 A151304 A151305 * A151307 A151308 A151309

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved