A041367 Denominators of continued fraction convergents to sqrt(198).

1, 14, 393, 5516, 154841, 2173290, 61006961, 856270744, 24036587793, 337368499846, 9470354583481, 132922332668580, 3731295669303721, 52371061702920674, 1470121023351082593, 20634065388618076976, 579223951904657237921, 8129769392053819407870

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,394,0,-1).

Formula

G.f.: -(x^2-14*x-1) / (x^4-394*x^2+1). - Colin Barker, Nov 16 2013

a(n) = 394*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[198], 30]] (* Harvey P. Dale, May 14 2013 *)
CoefficientList[Series[(1 + 14 x - x^2)/(x^4 - 394 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 16 2013 *)

Prog

(Magma) I:=[1, 14, 393, 5516]; [n le 4 select I[n] else 394*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041366, A040183.

Sequence in context: A097310 A223003 A228185 * A041364 A353609 A222904

Adjacent sequences: A041364 A041365 A041366 * A041368 A041369 A041370

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved