A150002 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, 0, 1)}.

1, 2, 5, 17, 60, 216, 814, 3207, 12825, 51562, 212425, 886744, 3711524, 15720371, 67150582, 288177213, 1244820633, 5402409852, 23563033358, 103220279392, 453516014870, 2000865601672, 8855020484585, 39286129387382, 174847836357748, 779928429088750, 3486920813753920, 15626514676720165

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, -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: A232217 A150000 A150001 * A150003 A150004 A150005

Adjacent sequences: A149999 A150000 A150001 * A150003 A150004 A150005

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved