A151055 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, 1), (0, 0, 1), (0, 1, 0), (1, 1, 0)}.

1, 3, 10, 37, 146, 596, 2488, 10577, 45621, 198971, 875546, 3881695, 17319136, 77692349, 350149137, 1584522530, 7196245139, 32786815893, 149806467269, 686239704863, 3150858847011, 14497664524101, 66834923897889, 308656720603898, 1427755641162334, 6614301325059226, 30684435986997431

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A052818 A299501 A226434 * A151056 A109081 A366231

Adjacent sequences: A151052 A151053 A151054 * A151056 A151057 A151058

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved