A148165 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, 0, 0), (-1, 1, 1), (0, -1, 1), (0, 1, 0), (1, 0, -1)}.

1, 1, 2, 4, 11, 31, 99, 320, 1107, 3917, 14398, 53921, 206822, 806398, 3196349, 12836214, 52180956, 214379114, 889187595, 3719706413, 15680492493, 66565341993, 284375168428, 1221963370108, 5278759630868, 22915612856972, 99928797488909, 437585962475297, 1923610987289162, 8486612734877707

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, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148164 A364594 A213091 * A148166 A148167 A148168

Adjacent sequences: A148162 A148163 A148164 * A148166 A148167 A148168

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved