A148070 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, -1, 1), (-1, 1, -1), (-1, 1, 1), (1, 0, 0)}.

1, 1, 2, 3, 12, 25, 97, 217, 984, 2409, 10215, 25487, 118874, 312013, 1396444, 3700827, 17618644, 48201953, 221644603, 608941279, 2931135298, 8236542965, 38529196470, 108470810209, 526019556566, 1506349925585, 7129197496267, 20427829442487, 99578663297064, 289201492121849, 1380244537295549, 4008026266125961

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A148067 A148068 A148069 * A187994 A016021 A173669

Adjacent sequences: A148067 A148068 A148069 * A148071 A148072 A148073

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved