A280761 Solutions y_n to the negative Pell equation y^2 = 72*x^2 - 8.

8, 280, 9512, 323128, 10976840, 372889432, 12667263848, 430314081400, 14618011503752, 496582077046168, 16869172608065960, 573055286597196472, 19467010571696614088, 661305304151087682520, 22464913330565284591592, 763145747935068588431608

Offset: 0

Author

N. J. A. Sloane, Jan 16 2017

Keywords

• nonn
• easy

Comments

Although this is a list, it has offset zero because one of the references numbered the solutions starting at 0.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..652
• S. Vidhyalakshmi, V. Krithika, K. Agalya, On The Negative Pell Equation y^2 = 72*x^2 - 8, International Journal of Emerging Technologies in Engineering Research (IJETER), Volume 4, Issue 2, February (2016).
• Index entries for linear recurrences with constant coefficients, signature (34,-1).

Crossrefs

For the x_n values see A077420.

Programs

Magma

I:=[8,280]; [n le 2 select I[n] else 34*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jan 18 2017

Mathematica

LinearRecurrence[{34, -1}, {8, 280}, 20] (* Vincenzo Librandi, Jan 18 2017 *)

PARI

a(n)=([0,1;-1,34]^n*[-8;8])[1,1] \\ Charles R Greathouse IV, Jan 17 2017

Formula

G.f.: 8*(1 + x)/(1 - 34*x + x^2). - Ilya Gutkovskiy, Jan 17 2017

a(n) = 34*a(n-1) - a(n-2), a(0)=8, a(1)=280. - Seiichi Manyama, Jan 17 2017

a(n) = (17+12*sqrt(2))^(-n)*(-4-3*sqrt(2) + (-4+3*sqrt(2))*(17+12*sqrt(2))^(2*n)) for n>0. - Colin Barker, Jan 17 2017

Extensions

More terms from Ilya Gutkovskiy, Jan 17 2017