A149867 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, 1), (-1, 1, -1), (0, 0, 1), (0, 1, 0), (1, -1, 0)}.

1, 2, 5, 13, 40, 134, 467, 1681, 6230, 23698, 91781, 361474, 1444421, 5838953, 23855627, 98385021, 409057415, 1713260510, 7223645090, 30637979060, 130649823315, 559905201444, 2410332888720, 10419393878406, 45214717684925, 196904962166692, 860326758933089, 3770559907597927, 16572613244060271

Offset

0,2

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A149865 A174146 A149866 * A062704 A274909 A263308

Adjacent sequences: A149864 A149865 A149866 * A149868 A149869 A149870

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved