A150598 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), (0, 0, -1), (0, 1, 0), (1, 1, 1)}.

1, 2, 7, 27, 109, 450, 1903, 8194, 35741, 157344, 697999, 3116893, 13996825, 63151172, 286073655, 1300481403, 5930501397, 27120076624, 124329033703, 571252051435, 2630067103881, 12131456702272, 56052949780143, 259396236118322, 1202143479190801, 5578668648467654, 25920643781424351, 120577281586873305

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, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A150596 A026726 A150597 * A026759 A361778 A150599

Adjacent sequences: A150595 A150596 A150597 * A150599 A150600 A150601

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved