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A041616 Numerators of continued fraction convergents to sqrt(327). 2
18, 217, 7830, 94177, 3398202, 40872601, 1474811838, 17738614657, 640064939490, 7698517888537, 277786708926822, 3341139025010401, 120558791609301258, 1450046638336625497, 52322237771727819150, 629316899899070455297, 22707730634138264209842 (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, 434, 0, -1).

FORMULA

G.f.: -(x^3-18*x^2-217*x-18)/(x^4-434*x^2+1). - Vincenzo Librandi, Nov 05 2013

a(n) = 434*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 05 2013

MATHEMATICA

Numerator[Convergents[Sqrt[327], 30]] (* or *) CoefficientList[Series[-(x^3 - 18 x^2 - 217 x - 18)/(x^4 - 434 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 05 2013 *)

LinearRecurrence[{0, 434, 0, -1}, {18, 217, 7830, 94177}, 20] (* Harvey P. Dale, Sep 10 2019 *)

PROG

(MAGMA) I:=[18, 217, 7830, 94177]; [n le 4 select I[n] else 434*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 05 2013

CROSSREFS

Cf. A041617.

Sequence in context: A021503 A025470 A046915 * A224296 A019333 A021454

Adjacent sequences:  A041613 A041614 A041615 * A041617 A041618 A041619

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 09 2013

STATUS

approved

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)