A150845 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, 1), (0, -1, 1), (0, 1, -1), (0, 1, 1), (1, 1, 0)}.

1, 2, 8, 32, 139, 618, 2815, 13017, 60855, 287001, 1362415, 6502201, 31167650, 149934312, 723476714, 3499963998, 16969632025, 82436773668, 401150765071, 1955002514510, 9540432897408, 46613349333715, 227993425528368, 1116247039256627, 5469986043680742, 26826680102548173, 131665972445904744

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A141380 A151304 A151828 * A150846 A150847 A150848

Adjacent sequences: A150842 A150843 A150844 * A150846 A150847 A150848

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved