A148318 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, 0, 1), (0, 0, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 5, 14, 39, 125, 406, 1377, 4764, 17164, 62469, 231943, 874618, 3351026, 12947298, 50620338, 199901919, 795986823, 3191015723, 12892664497, 52428537370, 214363751334, 881152162009, 3641565202414, 15117031897106, 63011652669118, 263740777264448, 1108178456066511, 4671918165041722

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[-1 + i, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A317553 A148316 A148317 * A148319 A126219 A320568

Adjacent sequences: A148315 A148316 A148317 * A148319 A148320 A148321

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved