A041416 Numerators of continued fraction convergents to sqrt(223).

14, 15, 209, 224, 6481, 6705, 93646, 100351, 2903474, 3003825, 41953199, 44957024, 1300749871, 1345706895, 18794939506, 20140646401, 582733038734, 602873685135, 8420090945489, 9022964630624

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