A132594 Values X satisfying the equation: X(X + 1) - 7*Y^2 = 0.

0, 63, 16128, 4096575, 1040514048, 264286471743, 67127723308800, 17050177433963583, 4330677940503441408, 1099975146710440154175, 279389356586511295719168, 70963796597827158672514623

Offset: 0

Author

Mohamed Bouhamida, Nov 14 2007

Keywords

• nonn

Comments

The full set of integer solutions to this equation consists of the pairs [X(i),Y(i)] = [1+-A001081(i), Y(i)=A001080(i)]. The present generates every second one of them: a(n) = [A001081(2n)-1]/2. - R. J. Mathar, Nov 20 2007

Links

• Index entries for linear recurrences with constant coefficients, signature (255, -255, 1).

Crossrefs

Cf. A007654.

Cf. A001080, A001081.

Programs

Mathematica

LinearRecurrence[{255,-255,1},{0,63,16128},20] (* Harvey P. Dale, Dec 15 2012 *)

Formula

a(0)=0, a(1)=63 and a(n)=254*a(n-1) - a(n-2) + 126.

G.f.: -63*x*(1+x)/(-1+x)/(1-254*x+x^2). a(n) = [A001081(2n)-1]/2. - R. J. Mathar, Nov 20 2007

a(0)=0, a(1)=63, a(2)=16128, a(n)=255*a(n-1)-255*a(n-2)+a(n-3). - Harvey P. Dale, Dec 15 2012

Extensions

More terms from Max Alekseyev, Nov 13 2009