A150867 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, 0, 1), (1, -1, 0), (1, 0, -1), (1, 1, 1)}

1, 2, 8, 33, 144, 646, 2956, 13714, 64303, 303914, 1445380, 6908740, 33159727, 159704801, 771417955, 3735457375, 18127282503, 88132763487, 429200044451, 2093234549671, 10222171723376, 49977833439139, 244608107536211, 1198341604700467, 5875836597723381, 28834053134536693, 141599014370814598

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[-1 + i, 1 + j, k, -1 + n] + aux[i, 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: A099015 A150865 A150866 * A255951 A150868 A150869

Adjacent sequences: A150864 A150865 A150866 * A150868 A150869 A150870

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved