A245264 Number of numbers in n-th generation of the tree of Gaussian rationals at A233696.

1, 2, 6, 12, 26, 53, 110, 231, 483, 1013, 2125, 4445, 9307, 19487, 40802, 85439, 178910, 374622, 784426, 1642522

Offset: 1

Author

Clark Kimberling, Jul 15 2014

Keywords

• nonn
• more

Comments

A233696 gives rules for constructing the Gaussian rationals in generations as follows: g(1) = {0}, and for n > 1, if x is in g(n-1) then x+1, i*x, and 1/x (for x not 0) are in g(n), except for those that are in g(j) for some j < n. Conjecture: 2 < lim(|g(n+1)|/|g(n)|) < 3.

Examples

			g(1) = {1}, so a(n) = 1; g(2) = {2,i}, so a(n) = 2; g(3) = {3, 1/2, 2*i, 1+i, -i, -1}, so a(3) = 6.
		

Crossrefs

Cf. A233696.

Programs

Mathematica

x = {0}; lenX = {}; Off[Power::infy]; Do[{x = DeleteDuplicates[    Flatten[Transpose[{x, x + 1, 1/x, I*x} /. ComplexInfinity -> 0]]], AppendTo[lenX, Length[x]]}, {15}]; On[Power::infy]; Join[{1}, Differences[lenX]]  (* Peter J. C. Moses, Dec 21 2013 *)