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A042306 Numerators of continued fraction convergents to sqrt(680). 2
26, 339, 17654, 229841, 11969386, 155831859, 8115226054, 105653770561, 5502111295226, 71633100608499, 3730423342937174, 48567136558791761, 2529221524400108746, 32928446953760205459, 1714808463119930792614 (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 (0,678,0,-1).

FORMULA

G.f.: (26 +339*x +26*x^2 -x^3)/(1 -678*x^2 +x^4). - Vincenzo Librandi Nov 21 2013

a(n) = 678*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 21 2013

MATHEMATICA

Numerator[Convergents[Sqrt[680], 30]] (* or *) CoefficientList[Series[(26 + 339 x + 26 x^2 - x^3)/(1 - 678 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)

PROG

(MAGMA) I:=[26, 339, 17654, 229841]; [n le 4 select I[n] else 678*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

CROSSREFS

Cf. A042307.

Sequence in context: A126919 A035708 A252826 * A329300 A053494 A054938

Adjacent sequences:  A042303 A042304 A042305 * A042307 A042308 A042309

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified January 25 16:01 EST 2022. Contains 350572 sequences. (Running on oeis4.)