A149507 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, -1), (-1, 0, 0), (0, -1, -1), (1, 1, 1)}.

1, 1, 5, 11, 47, 155, 567, 2221, 8173, 32497, 128021, 500621, 2045881, 8159033, 33233365, 136610895, 556058415, 2309390411, 9545735783, 39570216519, 165775628203, 690570644667, 2900036643435, 12206706417779, 51300646746555, 217150025395355, 917877590444083, 3888524712012907

Offset

0,3

Links

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

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149504 A149505 A149506 * A149508 A149509 A149510

Adjacent sequences: A149504 A149505 A149506 * A149508 A149509 A149510

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved