A150021 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, 1), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 5, 18, 67, 255, 1051, 4369, 18572, 80952, 354452, 1578206, 7087756, 32022176, 146097555, 669267386, 3084216216, 14286647804, 66396900479, 309990281251, 1451626208083, 6818529025761, 32126482382026, 151710234242601, 718259705285107, 3407732027062404, 16199219318914725, 77157761484968208

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A005753 A150020 A144721 * A150022 A150023 A150024

Adjacent sequences: A150018 A150019 A150020 * A150022 A150023 A150024

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved