A149732 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, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 75, 301, 1313, 5779, 26021, 118653, 545231, 2525549, 11788379, 55289461, 260927137, 1235788601, 5876795881, 28036136445, 134127337005, 643415715839, 3093416512511, 14904311410713, 71946402682733, 347889753790277, 1684869526253279, 8171554691807099, 39684352873993871, 192957177241489093

Offset

0,3

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A282963 A149730 A149731 * A149733 A149734 A149735

Adjacent sequences: A149729 A149730 A149731 * A149733 A149734 A149735

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved