A150608 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, 0, 0), (0, 1, 1), (1, -1, 0), (1, 0, -1), (1, 0, 0)}.

1, 2, 7, 27, 111, 474, 2077, 9296, 42201, 193760, 897717, 4189777, 19674643, 92860286, 440194367, 2094517473, 9998494197, 47865696280, 229724000261, 1104997603827, 5325819388111, 25715495218920, 124369010495551, 602384211870832, 2921616385087469, 14187693328434280, 68975724928581329

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A150605 A150606 A150607 * A150609 A150610 A150611

Adjacent sequences: A150605 A150606 A150607 * A150609 A150610 A150611

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved