A148876 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, 0, 1), (-1, 1, 1), (0, 1, -1), (1, -1, 1), (1, 0, 0)}.

1, 1, 3, 8, 29, 107, 431, 1784, 7638, 33420, 148739, 671858, 3068426, 14150462, 65767886, 307751287, 1448287916, 6849461114, 32532585554, 155097851229, 741865738329, 3558874732733, 17117063268783, 82519294654685, 398648382352128, 1929497558550710, 9354947802017698, 45427035668583344

Offset

0,3

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A022017 A148875 A338306 * A245889 A350907 A013309

Adjacent sequences: A148873 A148874 A148875 * A148877 A148878 A148879

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved