A148099 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, 1), (0, -1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 4, 10, 26, 76, 223, 702, 2214, 7304, 24164, 82489, 282164, 987881, 3463409, 12359141, 44151318, 159911910, 579698430, 2124693327, 7792875067, 28839353888, 106787736502, 398354778453, 1486699269986, 5582988776700, 20973971137343, 79208990291815, 299233839402802, 1135531152080614, 4310296717819132

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A049401 A294672 A239077 * A007579 A239078 A303930

Adjacent sequences: A148096 A148097 A148098 * A148100 A148101 A148102

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved