A150070 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, 0), (0, 0, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 6, 18, 64, 220, 782, 2824, 10328, 38306, 142388, 533832, 2011048, 7609034, 28938148, 110276428, 421716538, 1616589438, 6211475088, 23925481704, 92285891638, 356644978016, 1380284689858, 5349558200316, 20763135142878, 80668088650424, 313779804455788, 1221721443853960, 4761378554236090

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A150067 A150068 A150069 * A150071 A265945 A007454

Adjacent sequences: A150067 A150068 A150069 * A150071 A150072 A150073

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved