A148234 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, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 13, 34, 116, 330, 1162, 3536, 12877, 41066, 151769, 498166, 1860262, 6254556, 23590016, 80834615, 306837983, 1066600624, 4068927054, 14319207670, 54880379628, 195141810984, 750525883409, 2691555567339, 10382014415381, 37512878118392, 145085352407058, 527672333478588, 2045307592522895

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, j, 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: A148231 A148232 A148233 * A284335 A192443 A189590

Adjacent sequences: A148231 A148232 A148233 * A148235 A148236 A148237

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved