A150866 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, 0), (0, -1, 1), (0, 0, 1), (1, 0, -1), (1, 1, 1)}

1, 2, 8, 33, 144, 644, 2945, 13646, 63945, 302020, 1435617, 6859049, 32909060, 158447592, 765143817, 3704246334, 17972416827, 87365730777, 425406479062, 2074492249456, 10129646663572, 49521333174388, 242356791408169, 1187242065952816, 5821123709237361, 28564388975864433, 140269982156324898

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, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A279014 A099015 A150865 * A150867 A255951 A150868

Adjacent sequences: A150863 A150864 A150865 * A150867 A150868 A150869

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved