A148146 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, 0, 0), (0, -1, 1), (0, 1, 0), (1, 1, -1)}.

1, 1, 2, 4, 11, 29, 92, 282, 937, 3139, 10935, 38567, 139993, 512016, 1906146, 7189104, 27356563, 105196897, 408659119, 1596945488, 6291492797, 24971494328, 99570362528, 399510927609, 1612263534411, 6530008768311, 26580348708141, 108693681730104, 445784218670726, 1835751406440979

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[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A316768 A052831 A339834 * A148147 A298269 A148148

Adjacent sequences: A148143 A148144 A148145 * A148147 A148148 A148149

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved