A150175 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, 1), (-1, 1, 0), (0, 0, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 6, 20, 77, 295, 1189, 4867, 20499, 87115, 375222, 1631334, 7157895, 31624642, 140559349, 628073412, 2819894070, 12713368702, 57529575906, 261182939740, 1189316854038, 5430369426914, 24855857357875, 114026285378079, 524169608763114, 2414144401894739, 11138231425006868, 51472304686019227

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A195254 A150173 A150174 * A150176 A148484 A148485

Adjacent sequences: A150172 A150173 A150174 * A150176 A150177 A150178

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved