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A256793 Numbers whose minimal alternating squares representation has positive trace.

%I A256793 #6 Apr 14 2015 11:04:59
%S A256793 2,3,5,8,10,12,15,18,19,21,24,27,29,30,32,35,38,40,42,43,45,48,50,51,
%T A256793 53,55,57,58,60,63,65,67,68,70,72,74,75,77,80,83,84,86,87,89,91,93,94,
%U A256793 96,99,101,104,105,107,108,110,112,114,115,117,120,122,124
%N A256793 Numbers whose minimal alternating squares representation has positive trace.
%C A256793 See A256789 for definitions.
%H A256793 Clark Kimberling, <a href="/A256793/b256793.txt">Table of n, a(n) for n = 1..1000</a>
%e A256793 R(1) = 1; trace = 1, positive.
%e A256793 R(2) = 4 - 2; trace = -2, negative.
%e A256793 R(3) = 4 - 1; trace = -1, negative.
%t A256793 b[n_] := n^2; bb = Table[b[n], {n, 0, 1000}];
%t A256793 s[n_] := Table[b[n], {k, 1, 2 n - 1}];
%t A256793 h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
%t A256793 g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2};
%t A256793 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
%t A256793 Table[r[n], {n, 0, 120}] (* A256789 *)
%t A256793 u = Flatten[Table[Last[r[n]], {n, 1, 1000}]];  (* A256791 *)
%t A256793 Select[Range[800], u[[#]] > 0 &] (* A256792 *)
%t A256793 Select[Range[800], u[[#]] < 0 &] (* A256793 *)
%Y A256793 Cf. A256789, A256792 (complement).
%K A256793 nonn,easy
%O A256793 1,1
%A A256793 _Clark Kimberling_, Apr 13 2015