A041141 Denominators of continued fraction convergents to sqrt(79).

1, 1, 8, 9, 152, 161, 1279, 1440, 24319, 25759, 204632, 230391, 3890888, 4121279, 32739841, 36861120, 622517761, 659378881, 5238169928, 5897548809, 99598950872, 105496499681, 838074448639, 943570948320, 15935209621759, 16878780570079

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,160,0,0,0,-1).

Crossrefs

Cf. A041140, A010157, A020836, A010531.

Programs

Magma

I:=[1,1,8,9,152,161,1279,1440]; [n le 8 select I[n] else 160*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Mathematica

Denominator/@Convergents[Sqrt[79], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^2 - x - 1) (x^4 + 9 x^2 + 1)/(x^8 - 160 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0,0,0,160,0,0,0,-1},{1,1,8,9,152,161,1279,1440},40] (* Harvey P. Dale, Aug 09 2021 *)

Formula

G.f.: -(x^2-x-1)*(x^4+9*x^2+1) / (x^8-160*x^4+1). - Colin Barker, Nov 13 2013

a(n) = 160*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013