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%I #17 Nov 06 2018 04:31:29
%S 1,2,6,12,26,53,110,231,483,1013,2125,4445,9307,19487,40802,85439,
%T 178910,374622,784426,1642522
%N Number of numbers in n-th generation of the tree of Gaussian rationals at A233696.
%C 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.
%e 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.
%t 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 *)
%Y Cf. A233696.
%K nonn,more
%O 1,2
%A _Clark Kimberling_, Jul 15 2014
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