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A042080 Numerators of continued fraction convergents to sqrt(564). 2
23, 24, 71, 95, 4441, 4536, 13513, 18049, 843767, 861816, 2567399, 3429215, 160311289, 163740504, 487792297, 651532801, 30458301143, 31109833944, 92677969031, 123787802975, 5786916905881, 5910704708856 (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 (0,0,0,190,0,0,0,-1).

FORMULA

G.f.: -(x^7 - 23*x^6 + 24*x^5 - 71*x^4 - 95*x^3 - 71*x^2 -24*x - 23)/(x^8 - 190*x^4 + 1). - Vincenzo Librandi, Nov 16 2013

a(n) = 190*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 16 2013

MATHEMATICA

Numerator[Convergents[Sqrt[564], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 71 x^4 - 95 x^3 - 71 x^2 - 24 x - 23)/(x^8 - 190 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)

LinearRecurrence[{0, 0, 0, 190, 0, 0, 0, -1}, {23, 24, 71, 95, 4441, 4536, 13513, 18049}, 30] (* Harvey P. Dale, Apr 18 2015 *)

PROG

(MAGMA) I:=[23, 24, 71, 95, 4441, 4536, 13513, 18049]; [n le 8 select I[n] else 190*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

CROSSREFS

Cf. A042081.

Sequence in context: A042058 A045859 A042078 * A042076 A042074 A214510

Adjacent sequences:  A042077 A042078 A042079 * A042081 A042082 A042083

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 15 16:25 EST 2019. Contains 320136 sequences. (Running on oeis4.)