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A041563 Denominators of continued fraction convergents to sqrt(299). 2
1, 3, 7, 24, 823, 2493, 5809, 19920, 683089, 2069187, 4821463, 16533576, 566963047, 1717422717, 4001808481, 13722848160, 470578645921, 1425458785923, 3321496217767, 11389947439224, 390579709151383, 1183129074893373, 2756837858938129, 9453642651707760 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 19 13:08 EDT 2019. Contains 321330 sequences. (Running on oeis4.)