A149657 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, 0), (0, -1, 0), (0, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 59, 239, 977, 3915, 16303, 69667, 296063, 1267901, 5522509, 24150555, 105718063, 466486197, 2071291345, 9210313171, 41084031479, 184159624765, 827654854537, 3725656776357, 16820145214269, 76148179555723, 345270955147199, 1568181772886751, 7138177586911855, 32546518933448565

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, 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: A105392 A090857 A287804 * A149658 A149659 A149660

Adjacent sequences: A149654 A149655 A149656 * A149658 A149659 A149660

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved