A149702 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, 0), (-1, 0, 1), (1, -1, 0), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 69, 277, 1199, 4997, 22323, 96197, 433435, 1914391, 8686795, 38913039, 177843391, 804285853, 3695136351, 16839549393, 77665053029, 356072649163, 1647634680213, 7589339987379, 35217751634367, 162838988949557, 757466254449869, 3513570095624009, 16377908690599267, 76175870755112467

Offset

0,3

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[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A272743 A149700 A149701 * A273331 A149703 A149704

Adjacent sequences: A149699 A149700 A149701 * A149703 A149704 A149705

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved