A148465 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, 0), (0, -1, 1), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 6, 19, 61, 216, 789, 2960, 11439, 45114, 180779, 735676, 3030120, 12613335, 53004791, 224550436, 958227715, 4115750849, 17780103175, 77214818728, 336921319180, 1476478558914, 6495954222412, 28683344656932, 127075652153227, 564718190262450, 2516734088100503, 11245821481990912

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 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: A114627 A289591 A148464 * A148466 A094817 A033565

Adjacent sequences: A148462 A148463 A148464 * A148466 A148467 A148468

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved