A150224 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), (0, 0, -1), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 21, 84, 348, 1481, 6468, 28704, 129540, 591232, 2725221, 12661345, 59210568, 278508409, 1316337557, 6248468083, 29770699443, 142309486586, 682256163533, 3279330154213, 15799375611524, 76278746066478, 368972823724429, 1787862776781551, 8676751090788568, 42170206290003916, 205223499849964114

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[i, 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: A328435 A150222 A150223 * A150225 A123922 A350798

Adjacent sequences: A150221 A150222 A150223 * A150225 A150226 A150227

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved