A150876 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), (0, 1, -1), (1, -1, 1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 33, 147, 673, 3157, 15018, 72219, 349962, 1705743, 8350942, 41026930, 202115652, 997912715, 4935914463, 24450370176, 121265130550, 602048811255, 2991593112845, 14876177933404, 74020421610042, 368506069018971, 1835433703374390, 9145491023410741, 45585547373285910, 227289911949809065

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A150873 A150874 A150875 * A150877 A150878 A150879

Adjacent sequences: A150873 A150874 A150875 * A150877 A150878 A150879

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved