A149194 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, 0), (0, -1, 1), (0, 1, -1), (1, 1, 0)}.

1, 1, 4, 10, 38, 127, 493, 1849, 7444, 29523, 122641, 503166, 2139489, 8990962, 38889133, 166435151, 729268850, 3166004539, 14014630572, 61540779798, 274683353115, 1217425797984, 5471448336914, 24436690566099, 110465215458605, 496547674115096, 2255792311485189, 10195606252477070

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[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, 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: A149192 A032123 A149193 * A149195 A149196 A149197

Adjacent sequences: A149191 A149192 A149193 * A149195 A149196 A149197

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved