A151296 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, 0)}.

1, 2, 7, 26, 104, 436, 1878, 8285, 37144, 168793, 775209, 3591445, 16760364, 78696089, 371450137, 1761190032, 8383369989, 40042977165, 191846857887, 921629216986, 4438189698963, 21418876479779, 103570607307949, 501701667445534, 2434187911313517, 11827723470989792, 57548359992678038, 280350852928397935

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, j, -1 + n] + aux[-1 + 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: A345884 A150545 A150546 * A141370 A150547 A150548

Adjacent sequences: A151293 A151294 A151295 * A151297 A151298 A151299

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved