A150164 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, 0), (0, 1, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 6, 20, 75, 286, 1166, 4780, 20165, 85995, 371460, 1619327, 7120583, 31509317, 140326866, 628064132, 2823902816, 12748912424, 57759405138, 262530017621, 1196718820414, 5469335106100, 25056263179852, 115037888571988, 529212287160997, 2439036334073988, 11260074938277269, 52065063815182423

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, 1 + k, -1 + n] + aux[1 + i, j, 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: A150161 A150162 A150163 * A150165 A148482 A148483

Adjacent sequences: A150161 A150162 A150163 * A150165 A150166 A150167

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved