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A041416 Numerators of continued fraction convergents to sqrt(223). 2
14, 15, 209, 224, 6481, 6705, 93646, 100351, 2903474, 3003825, 41953199, 44957024, 1300749871, 1345706895, 18794939506, 20140646401, 582733038734, 602873685135, 8420090945489, 9022964630624 (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 (0,0,0,448,0,0,0,-1).

FORMULA

G.f.: (14 +15*x +209*x^2 +224*x^3 +209*x^4 -15*x^5 +14*x^6 -x^7) / (1 -448*x^4 +x^8). - Vincenzo Librandi, Nov 02 2013

a(0)=14, a(1)=15, a(2)=209, a(3)=224, a(4)=6481, a(5)=6705, a(6)=93646, a(7)=100351, a(n)=448*a(n-4)-a(n-8). - Harvey P. Dale, Jan 10 2016

MATHEMATICA

Numerator[Convergents[Sqrt[223], 30]] (* or *) CoefficientList[Series[(14 + 15 x + 209 x^2 + 224 x^3 + 209 x^4 - 15 x^5 + 14 x^6 - x^7)/(1 - 448 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 02 2013 *)

LinearRecurrence[{0, 0, 0, 448, 0, 0, 0, -1}, {14, 15, 209, 224, 6481, 6705, 93646, 100351}, 30] (* Harvey P. Dale, Jan 10 2016 *)

CROSSREFS

Cf. A041417.

Sequence in context: A041414 A033050 A225757 * A041417 A041418 A042733

Adjacent sequences:  A041413 A041414 A041415 * A041417 A041418 A041419

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 20 21:05 EST 2019. Contains 320347 sequences. (Running on oeis4.)