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

0,3

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A041140, A010157, A020836, A010531.

Sequence in context: A175556 A165467 A239584 * A041142 A307947 A175849

Adjacent sequences: A041138 A041139 A041140 * A041142 A041143 A041144

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved