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A256792 Numbers whose minimal alternating squares representation has positive trace.

%I A256792 #7 Apr 14 2015 11:04:49
%S A256792 1,4,6,7,9,11,13,14,16,17,20,22,23,25,26,28,31,33,34,36,37,39,41,44,
%T A256792 46,47,49,52,54,56,59,61,62,64,66,69,71,73,76,78,79,81,82,85,88,90,92,
%U A256792 95,97,98,100,102,103,106,109,111,113,116,118,119,121,123,125
%N A256792 Numbers whose minimal alternating squares representation has positive trace.
%C A256792 See A256789 for definitions.
%H A256792 Clark Kimberling, <a href="/A256792/b256792.txt">Table of n, a(n) for n = 1..1000</a>
%e A256792 R(1) = 1; trace = 1, positive.
%e A256792 R(2) = 4 - 2; trace = -2, negative.
%e A256792 R(3) = 4 - 1; trace = -1, negative.
%t A256792 b[n_] := n^2; bb = Table[b[n], {n, 0, 1000}];
%t A256792 s[n_] := Table[b[n], {k, 1, 2 n - 1}];
%t A256792 h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
%t A256792 g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2};
%t A256792 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
%t A256792 Table[r[n], {n, 0, 120}] (* A256789 *)
%t A256792 u = Flatten[Table[Last[r[n]], {n, 1, 1000}]];  (* A256791 *)
%t A256792 Select[Range[800], u[[#]] > 0 &] (* A256792 *)
%t A256792 Select[Range[800], u[[#]] < 0 &] (* A256793 *)
%Y A256792 Cf. A256789, A256793 (complement).
%K A256792 nonn,easy
%O A256792 1,2
%A A256792 _Clark Kimberling_, Apr 13 2015