A151042 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, 1, -1), (0, 1, 0), (0, 1, 1), (1, 0, 0)}.

1, 3, 9, 33, 129, 511, 2110, 8883, 37770, 163078, 711157, 3122349, 13813470, 61489000, 274994926, 1235534550, 5574180288, 25233308678, 114589332333, 521906125367, 2383113544526, 10907286930454, 50031574548984, 229948117747006, 1058783283652308, 4883463242267293, 22559695965552386, 104369418822478204

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A151039 A151040 A151041 * A087289 A084508 A151043

Adjacent sequences: A151039 A151040 A151041 * A151043 A151044 A151045

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved