A151109 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), (1, 0, 0), (1, 0, 1)}.

1, 3, 11, 45, 187, 813, 3595, 16129, 73455, 337045, 1560531, 7271537, 34061735, 160372701, 757970843, 3595687081, 17111115759, 81651588021, 390627636835, 1872913492353, 8998295638711, 43311574341005, 208819980112683, 1008354117957401, 4876013903788671, 23609343188579301, 114453003449887219

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 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: A073590 A144637 A369839 * A151110 A151111 A292278

Adjacent sequences: A151106 A151107 A151108 * A151110 A151111 A151112

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved