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A042778 Numerators of continued fraction convergents to sqrt(920). 2
30, 91, 5490, 16561, 999150, 3014011, 181839810, 548533441, 33093846270, 99830072251, 6022898181330, 18168524616241, 1096134375155790, 3306571650083611, 199490433380172450, 601777871790600961, 36306162740816230110, 109520266094239291291, 6607522128395173707570 (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 (0,182,0,-1).

FORMULA

G.f.: (30 + 91*x + 30*x^2 - x^3)/(1 - 182*x^2 + x^4). - Vincenzo Librandi, Dec 04 2013, simplified by Colin Barker, Dec 23 2013

a(n) = 33122*a(n-4) - a(n-8) = 182*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 04 2013, reduced by Bruno Berselli, Dec 23 2013

MATHEMATICA

Numerator[Convergents[Sqrt[920], 30]] (* or *) CoefficientList[Series[(30 + 91 x + 30 x^2 - x^3)/(1 - 182 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 04 2013 *)

PROG

(MAGMA) I:=[30, 91, 5490, 16561]; [n le 4 select I[n] else 182*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 04 2013, reduced by Bruno Berselli, Dec 23 2013

CROSSREFS

Cf. A042779, A040889.

Sequence in context: A306121 A042774 A042776 * A031212 A165133 A044217

Adjacent sequences:  A042775 A042776 A042777 * A042779 A042780 A042781

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vincenzo Librandi, Dec 04 2013

STATUS

approved

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Last modified March 20 05:29 EDT 2019. Contains 321344 sequences. (Running on oeis4.)