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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
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
Sequence in context: A019055 A300515 A041045 * A042657 A031875 A157817
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 19 2013
STATUS
approved

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Last modified April 23 16:38 EDT 2024. Contains 371916 sequences. (Running on oeis4.)