A150407 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), (0, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 2, 7, 24, 93, 376, 1560, 6606, 28459, 124092, 546417, 2424978, 10834083, 48674504, 219721426, 995917393, 4530389392, 20673892690, 94608077696, 434035171255, 1995741367560, 9195456939078, 42447487636534, 196277742105506, 909013161586392, 4215958362164549, 19579546434216768, 91043208191401018

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, -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: A150404 A150405 A150406 * A317130 A150408 A150409

Adjacent sequences: A150404 A150405 A150406 * A150408 A150409 A150410

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved