A148380 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), (0, -1, 1), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 5, 16, 48, 160, 531, 1870, 6524, 23574, 84928, 312864, 1150386, 4293426, 16017483, 60369252, 227575756, 864161558, 3283431528, 12541744032, 47943856414, 184003950632, 706809708056, 2723270814302, 10501894049804, 40594747787924, 157054821466912, 608764065331656, 2361608766307196

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, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[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: A148378 A148379 A257970 * A210696 A005497 A148381

Adjacent sequences: A148377 A148378 A148379 * A148381 A148382 A148383

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved