A148324 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), (-1, 1, 0), (0, 0, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 2, 5, 14, 41, 136, 453, 1625, 5916, 22413, 86262, 341145, 1364600, 5575554, 22970257, 96219317, 405776643, 1733558159, 7449181815, 32339997454, 141107551277, 620848468901, 2743496180912, 12207546137457, 54524169872592, 244949648545018, 1104077076016340, 5001154826725525

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A287968 A148322 A148323 * A000660 A148325 A281594

Adjacent sequences: A148321 A148322 A148323 * A148325 A148326 A148327

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved