A150918 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, 0, 1), (1, -1, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 32, 150, 629, 2981, 13333, 63815, 294399, 1419620, 6668577, 32325597, 153659636, 747701911, 3583832819, 17489677420, 84342378614, 412554594772, 1998755333864, 9795109320394, 47628515125998, 233772469672562, 1140037690073939, 5602971263909291, 27389380521686264, 134763936157530707

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150915 A150916 A150917 * A150919 A150920 A013501

Adjacent sequences: A150915 A150916 A150917 * A150919 A150920 A150921

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved