A244713 Positive numbers primitively represented by the binary quadratic form (1, 1, -2).
1, 4, 7, 10, 13, 16, 18, 19, 22, 25, 27, 28, 31, 34, 37, 40, 43, 45, 46, 49, 52, 54, 55, 58, 61, 64, 67, 70, 72, 73, 76, 79, 81, 82, 85, 88, 91, 94, 97, 99, 100, 103, 106, 108, 109, 112, 115, 118, 121, 124, 126, 127, 130, 133, 135, 136, 139, 142, 145, 148, 151
Offset: 1
Keywords
Links
- Ray Chandler, Table of n, a(n) for n = 1..10000
- N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
Programs
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Mathematica
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 *)
Formula
Conjectures from Colin Barker, Oct 31 2016: (Start)
a(n) = a(n-1)+a(n-11)-a(n-12) for n>12.
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)).
(End)
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