A041563 Denominators of continued fraction convergents to sqrt(299).

1, 3, 7, 24, 823, 2493, 5809, 19920, 683089, 2069187, 4821463, 16533576, 566963047, 1717422717, 4001808481, 13722848160, 470578645921, 1425458785923, 3321496217767, 11389947439224, 390579709151383, 1183129074893373, 2756837858938129, 9453642651707760

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 830, 0, 0, 0, -1).

Formula

G.f.: -(x^2-3*x-1)*(x^4+8*x^2+1) / (x^8-830*x^4+1). - Colin Barker, Nov 19 2013

a(n) = 830*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[299], 30]] (* Harvey P. Dale, May 02 2012 *)
CoefficientList[Series[(1 + 3 x - x^2) (x^4 + 8 x^2 + 1)/(x^8 - 830 x^4+1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 3, 7, 24, 823, 2493, 5809, 19920]; [n le 8 select I[n] else 830*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041562, A040281.

Sequence in context: A019055 A300515 A041045 * A042657 A031875 A157817

Adjacent sequences: A041560 A041561 A041562 * A041564 A041565 A041566

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved