A149481 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, 0, 1), (-1, 1, 1), (1, -1, 0), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 13, 58, 223, 1035, 4385, 20837, 92832, 447686, 2056408, 10011840, 46924966, 229928748, 1092889534, 5379243634, 25829380711, 127549443682, 617106718099, 3054805216270, 14865442568292, 73723871989651, 360379717873853, 1789852017157827, 8780525377135672, 43658728589830775, 214793394110780838

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A151481 A283612 A039626 * A149482 A149483 A149484

Adjacent sequences: A149478 A149479 A149480 * A149482 A149483 A149484

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved