A151330 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, 0), (1, 1)}.

1, 3, 17, 95, 577, 3591, 22913, 148423, 973297, 6440919, 42938417, 287943719, 1940382241, 13129012247, 89139404337, 606990586023, 4143744218529, 28350360516935, 194338902989281, 1334433092793687, 9176683714637953, 63190999089974583, 435656341477960785, 3006765235738762775

Offset

0,2

Links

Table of n, a(n) for n=0..23.

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[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + 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: A290925 A020056 A086842 * A370570 A302871 A010913

Adjacent sequences: A151327 A151328 A151329 * A151331 A151332 A151333

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved