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

1,2

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.

Links

Table of n, a(n) for n=1..20.

Example

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.

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 *)

Crossrefs

Cf. A233696.

Sequence in context: A246584 A054454 A084170 * A327477 A350294 A052971

Adjacent sequences: A245261 A245262 A245263 * A245265 A245266 A245267

Keyword

nonn,more

Author

Clark Kimberling, Jul 15 2014

Status

approved