%I #11 Nov 25 2015 21:22:02
%S 0,1,-2,2,-4,-1,3,4,-8,-6,-3,5,8,-16,-10,-7,-5,6,9,12,16,-32,-24,-18,
%T -15,-12,-9,7,10,13,14,17,20,32,-64,-40,-34,-31,-28,-26,-23,-20,-17,
%U -14,-11,11,15,18,21,24,30,33,36,48,64,-128,-96,-72,-66,-63,-60
%N Tree T generated by these rules: 0 is in T, and if x is in T, then x+1 and -2x are in T, with duplicates deleted as they occur.
%C Every integer occur in T exactly once, so that this is a permutation of the integers. Let g(0) = {0}, g(1) = {1}, g(2) = {-2,2}, g(3) = {-4,-1,3,4}, etc. The number |g(n)| of numbers in the n-th generation is a Fibonacci number except for g(3); see A264800.
%H Clark Kimberling, <a href="/A264799/b264799.txt">Table of n, a(n) for n = 0..10000</a>
%e Generations begin with
%e 0
%e 1
%e -2 2
%e -4 -1 3 4
%e -8 -6 -3 5 8
%e -16 -10 -7 -5 6 9 12 16
%t z = 10; t = Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, -2*#} &, #], 1]] &, {0}, z]]; s[0] = t[[1]]; s[n_] := s[n] = Union[t[[n]], s[n - 1]];
%t g[n_] := Complement[s[n], s[n - 1]]; g[1] = {0};
%t Table[Length[g[k]], {k, 1, z}] (* A264800 *)
%t u = Table[g[k], {k, 1, z}]
%t Flatten[u] (* A264799 *)
%Y Cf. A000045, A226080, A264800.
%K sign,tabf,easy
%O 0,3
%A _Clark Kimberling_, Nov 25 2015