A150112 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), (0, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 2, 6, 19, 70, 262, 1031, 4153, 17104, 71585, 303758, 1303324, 5645184, 24647181, 108364268, 479285899, 2131180012, 9520717770, 42710777994, 192323297051, 868946783064, 3938096694053, 17897424213394, 81546179597241, 372420902761982, 1704519540738366, 7816936108095650, 35914879901405947

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + 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: A150109 A150110 A150111 * A150113 A150114 A199128

Adjacent sequences: A150109 A150110 A150111 * A150113 A150114 A150115

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved