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A042808 Numerators of continued fraction convergents to sqrt(935). 2
30, 31, 61, 153, 214, 581, 795, 1376, 83355, 84731, 168086, 420903, 588989, 1598881, 2187870, 3786751, 229392930, 233179681, 462572611, 1158324903, 1620897514, 4400119931, 6021017445, 10421137376, 631289260005, 641710397381, 1272999657386, 3187709712153 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 2752, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: (30 +31*x +61*x^2 +153*x^3 +214*x^4 +581*x^5 +795*x^6 +1376*x^7 +795*x^8 -581*x^9 +214*x^10 -153*x^11 +61*x^12 -31*x^13 +30*x^14 -x^15)/(1 -2752*x^8 +x^16). - Vincenzo Librandi, Dec 05 2013

a(n) = 2752*a(n-8) - a(n-16) - Vincenzo Librandi, Dec 05 2013

MATHEMATICA

Numerator[Convergents[Sqrt[935], 30]] (* or *) CoefficientList[Series[(30 + 31 x + 61 x^2 + 153 x^3 + 214 x^4 + 581 x^5 + 795 x^6 + 1376 x^7 + 795 x^8 - 581 x^9 + 214 x^10 - 153 x^11 + 61 x^12 - 31 x^13 + 30 x^14 - x^15)/(1 - 2752 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 05 2013 *)

PROG

(MAGMA) I:=[30, 31, 61, 153, 214, 581, 795, 1376, 83355, 84731, 168086, 420903, 588989, 1598881, 2187870, 3786751]; [n le 16 select I[n] else 2752*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 05 2013

CROSSREFS

Cf. A042809.

Sequence in context: A042814 A042816 A042818 * A042810 A042806 A042804

Adjacent sequences:  A042805 A042806 A042807 * A042809 A042810 A042811

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Dec 05 2013

STATUS

approved

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Last modified February 15 20:46 EST 2019. Contains 320138 sequences. (Running on oeis4.)