A256793 Numbers whose minimal alternating squares representation has positive trace.

2, 3, 5, 8, 10, 12, 15, 18, 19, 21, 24, 27, 29, 30, 32, 35, 38, 40, 42, 43, 45, 48, 50, 51, 53, 55, 57, 58, 60, 63, 65, 67, 68, 70, 72, 74, 75, 77, 80, 83, 84, 86, 87, 89, 91, 93, 94, 96, 99, 101, 104, 105, 107, 108, 110, 112, 114, 115, 117, 120, 122, 124

Offset: 1

Author

Clark Kimberling, Apr 13 2015

Keywords

• nonn
• easy

Comments

See A256789 for definitions.

Examples

			R(1) = 1; trace = 1, positive.
R(2) = 4 - 2; trace = -2, negative.
R(3) = 4 - 1; trace = -1, negative.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A256789, A256792 (complement).

Programs

Mathematica

b[n_] := n^2; bb = Table[b[n], {n, 0, 1000}];
s[n_] := Table[b[n], {k, 1, 2 n - 1}];
h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
Table[r[n], {n, 0, 120}] (* A256789 *)
u = Flatten[Table[Last[r[n]], {n, 1, 1000}]];  (* A256791 *)
Select[Range[800], u[[#]] > 0 &] (* A256792 *)
Select[Range[800], u[[#]] < 0 &] (* A256793 *)