A148018 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, 0, 1), (0, 1, -1), (1, -1, -1)}.

1, 1, 2, 3, 8, 17, 46, 120, 345, 1022, 2910, 9040, 27530, 88493, 283253, 912384, 3037696, 9955390, 33803098, 113920402, 390162517, 1349732321, 4642227231, 16328414313, 56978655042, 202131478689, 717829790091, 2553299150122, 9196541401438, 32928272615601, 119572300555189, 433085570807293, 1577395594151588

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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, 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: A148015 A148016 A148017 * A148019 A148020 A148021

Adjacent sequences: A148015 A148016 A148017 * A148019 A148020 A148021

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved