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A256792
Numbers whose minimal alternating squares representation has positive trace.
4
1, 4, 6, 7, 9, 11, 13, 14, 16, 17, 20, 22, 23, 25, 26, 28, 31, 33, 34, 36, 37, 39, 41, 44, 46, 47, 49, 52, 54, 56, 59, 61, 62, 64, 66, 69, 71, 73, 76, 78, 79, 81, 82, 85, 88, 90, 92, 95, 97, 98, 100, 102, 103, 106, 109, 111, 113, 116, 118, 119, 121, 123, 125
OFFSET
1,2
COMMENTS
See A256789 for definitions.
LINKS
EXAMPLE
R(1) = 1; trace = 1, positive.
R(2) = 4 - 2; trace = -2, negative.
R(3) = 4 - 1; trace = -1, negative.
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 *)
CROSSREFS
Cf. A256789, A256793 (complement).
Sequence in context: A183870 A186497 A193627 * A367186 A345665 A343177
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 13 2015
STATUS
approved