A148248 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), (0, 1, 0), (1, -1, -1), (1, -1, 1)}.

1, 1, 2, 4, 13, 36, 120, 405, 1393, 4830, 17433, 63618, 233299, 874696, 3320439, 12653584, 48669008, 189332510, 739327998, 2899957479, 11465903125, 45547362769, 181415934245, 726323099412, 2921357333744, 11777518788194, 47635814780811, 193415913415674, 787208964488147, 3211068378099671

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + 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: A148245 A148246 A148247 * A148249 A148250 A148251

Adjacent sequences: A148245 A148246 A148247 * A148249 A148250 A148251

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved