A148612 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, 0, 1)}.

1, 1, 3, 6, 21, 53, 202, 573, 2294, 7006, 28944, 93034, 391864, 1309196, 5593893, 19242110, 83177233, 292817279, 1277239439, 4583036003, 20135459495, 73405731065, 324465065173, 1198819650283, 5326177488325, 19907188328591, 88831157902685, 335362062137753, 1502141510499395, 5721080073872425

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-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: A148609 A148610 A148611 * A098511 A354734 A112520

Adjacent sequences: A148609 A148610 A148611 * A148613 A148614 A148615

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved