A150317 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), (-1, 1, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 21, 90, 322, 1457, 5567, 26084, 104654, 496743, 2045612, 9842455, 41463219, 200634301, 857222498, 4176230658, 18078487719, 88343440571, 385849421800, 1892960818330, 8338436176740, 40984345622043, 181649839565480, 895071887418120, 3990926650596026, 19689616173526209, 88190114396086753

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A150314 A150315 A150316 * A150318 A150319 A150320

Adjacent sequences: A150314 A150315 A150316 * A150318 A150319 A150320

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved