A148851 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), (0, 0, -1), (0, 1, 1), (1, -1, 1)}.

1, 1, 3, 8, 28, 91, 339, 1219, 4701, 17939, 71573, 284089, 1157733, 4721259, 19569779, 81402649, 342160546, 1445001223, 6145007988, 26261712426, 112789021222, 486638853729, 2107738866605, 9165837675101, 39988572047898, 175057214787952, 768550521307934, 3383830890482911, 14937351793963389

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A148848 A148849 A148850 * A148852 A148853 A148854

Adjacent sequences: A148848 A148849 A148850 * A148852 A148853 A148854

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved