A151034 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, 0), (0, 0, 1), (0, 1, 0), (1, 0, 1)}.

1, 3, 9, 31, 117, 451, 1777, 7199, 29637, 123299, 518993, 2206159, 9445397, 40707171, 176521745, 769398527, 3368657701, 14810903779, 65363377937, 289425316975, 1285506346741, 5725875634595, 25570006950097, 114460194724255, 513500131303429, 2308442353517859, 10397462576136913, 46915044504633871

Offset

0,2

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A365113 A110136 A202180 * A151035 A151036 A073724

Adjacent sequences: A151031 A151032 A151033 * A151035 A151036 A151037

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved