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%I #13 Oct 31 2016 10:22:00
%S 1,4,7,10,13,16,18,19,22,25,27,28,31,34,37,40,43,45,46,49,52,54,55,58,
%T 61,64,67,70,72,73,76,79,81,82,85,88,91,94,97,99,100,103,106,108,109,
%U 112,115,118,121,124,126,127,130,133,135,136,139,142,145,148,151
%N Positive numbers primitively represented by the binary quadratic form (1, 1, -2).
%C Discriminant = 9.
%H Ray Chandler, <a href="/A244713/b244713.txt">Table of n, a(n) for n = 1..10000</a>
%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%F Conjectures from _Colin Barker_, Oct 31 2016: (Start)
%F a(n) = a(n-1)+a(n-11)-a(n-12) for n>12.
%F G.f.: (1 +2*x)*(1 +x +x^2)*(1 +x^3 +x^7) / ((1 -x)^2*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6 +x^7 +x^8 +x^9 +x^10)).
%F (End)
%t Reap[For[n = 1, n < 1000, n++, r = Reduce[x^2 + x y - 2 y^2 == n, {x, y}, Integers]; If[r =!= False, If[AnyTrue[{x, y} /. {ToRules[r /. C[1] -> 0]}, CoprimeQ @@ # &], Sow[n]]]]][[2, 1]] (* _Jean-François Alcover_, Oct 31 2016 *)
%Y Cf. A002476, A007645. A subsequence of A056991 and A242660.
%K nonn
%O 1,2
%A _Peter Luschny_, Jul 04 2014
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