A150122 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, -1, 0), (-1, 0, 0), (0, 0, 1), (1, 1, 0)}.

1, 2, 6, 20, 68, 250, 924, 3528, 13668, 53584, 213074, 852976, 3447882, 14021322, 57368826, 236006796, 975087356, 4046503078, 16851624666, 70419777860, 295160069720, 1240535072130, 5227287139952, 22076820929638, 93441027387480, 396272206161792, 1683637050747310, 7165509645578814

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, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A360219 A360294 A150121 * A150123 A082679 A094854

Adjacent sequences: A150119 A150120 A150121 * A150123 A150124 A150125

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved