A150402 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, 1), (-1, 0, 1), (0, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 2, 7, 24, 93, 363, 1497, 6207, 26461, 113443, 494208, 2163605, 9568525, 42495997, 190036750, 852878044, 3846664090, 17402240589, 79021622447, 359760117542, 1642665702785, 7517076646442, 34480546970663, 158463454209716, 729681420844286, 3365557841877427, 15548849162260961, 71939582316623193

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, -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: A150401 A003041 A026558 * A151295 A150403 A150404

Adjacent sequences: A150399 A150400 A150401 * A150403 A150404 A150405

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved