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A274455 Sequence (or tree) generated by these rules: 1 is in S, and if x is in S, then x -1 and 2*x are in S, and duplicates are deleted as they occur.

%I A274455 #4 Jun 26 2016 11:16:19
%S A274455 1,0,2,-1,4,-2,3,8,-3,-4,6,7,16,-6,-5,-8,5,12,14,15,32,-7,-12,-10,-9,
%T A274455 -16,10,11,24,13,28,30,31,64,-14,-13,-24,-11,-20,-18,-17,-32,9,20,22,
%U A274455 23,48,26,27,56,29,60,62,63,128,-15,-28,-26,-25,-48,-22,-21
%N A274455 Sequence (or tree) generated by these rules: 1 is in S, and if x is in S, then x -1 and 2*x are in S, and duplicates are deleted as they occur.
%C A274455 Every integer occurs exactly once.  The rules for this tree become identical to those for A232559 when "x + 1" is substituted for "x - 1".
%C A274455 For n > 3, the n-th generation has F(n) nodes, of which F(n-1) are positive and F(n-2) are negative, where F = A000045, the Fibonacci numbers.
%H A274455 Clark Kimberling, <a href="/A274455/b274455.txt">Table of n, a(n) for n = 1..10946</a>
%e A274455 Generation g(1) consists of the seed, 1; generation g(2) consists of 0 and 2 from which 0 begets -1 and 0, but this 0 is a duplicate and is removed, while 2 begets 1 and 4, with 1 removed, so that g(3) = {-1,4}.  Thereafter, g(4) = {-2,3,8}, g(5) = {-3,-4,6,7,16}, etc.
%t A274455 z = 12; g[1] = {1}; g[2] = {0, 2};
%t A274455 g[n_] := Riffle[g[n - 1] - 1, 2 g[n - 1]];
%t A274455 j[2] = Join[g[1], g[2]]; j[n_] := Join[j[n - 1], g[n]];
%t A274455 g1[n_] := DeleteDuplicates[DeleteCases[g[n], Alternatives @@ j[n - 1]]];
%t A274455 g1[1] = g[1]; g1[2] = g[2]; t = Flatten[Table[g1[n], {n, 1, z}]]  (*A274455*)
%Y A274455 Cf. A000045, A232559.
%K A274455 sign,easy
%O A274455 1,3
%A A274455 _Clark Kimberling_, Jun 23 2016