A149193 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, 0, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 10, 38, 127, 493, 1841, 7280, 28878, 116567, 478811, 1973493, 8272377, 34738919, 147542225, 629264252, 2700080188, 11655144044, 50463437540, 219806610774, 959526286345, 4208678301965, 18506049432901, 81640804619981, 361209023120827, 1601666859421432, 7122833707402200

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, 1 + j, -1 + k, -1 + n] + aux[i, 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: A149191 A149192 A032123 * A149194 A149195 A149196

Adjacent sequences: A149190 A149191 A149192 * A149194 A149195 A149196

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved