A148881 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, 1, 1), (0, 0, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 3, 8, 30, 96, 403, 1466, 6439, 25426, 114604, 476405, 2187128, 9410849, 43797442, 193201730, 908410384, 4083431156, 19351522407, 88275335700, 420946248654, 1942836289306, 9311177087202, 43384912071474, 208788198483504, 980475447765973, 4734900305936681, 22380831968092385, 108399898901413396

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[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148878 A148879 A148880 * A148882 A148883 A148884

Adjacent sequences: A148878 A148879 A148880 * A148882 A148883 A148884

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved