A151007 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), (0, 1, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 38, 179, 837, 4032, 19449, 95025, 464623, 2287118, 11267034, 55704847, 275630074, 1366658295, 6780839615, 33688009846, 167454085841, 833090376329, 4146412415578, 20649520773537, 102871682826652, 512701830585969, 2555952678681018, 12746059166008213, 63576222439713458, 317187359821712105

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[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: A151005 A105484 A151006 * A151008 A057647 A249925

Adjacent sequences: A151004 A151005 A151006 * A151008 A151009 A151010

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved