A041371 Denominators of continued fraction convergents to sqrt(200).

1, 7, 197, 1386, 39005, 274421, 7722793, 54333972, 1529074009, 10757852035, 302748930989, 2130000368958, 59942759261813, 421729315201649, 11868363584907985, 83500274409557544, 2349876047052519217, 16532632603777192063, 465263588952813896981

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,198,0,-1).

Formula

G.f.: -(x^2-7*x-1) / ((x^2-14*x-1)*(x^2+14*x-1)). - Colin Barker, Nov 16 2013

a(n) = 198*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[200], 30]] (* Vincenzo Librandi, Dec 16 2013 *)

Prog

(Magma) I:=[1, 7, 197, 1386]; [n le 4 select I[n] else 198*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041370, A040185.

Sequence in context: A156359 A128786 A034835 * A136675 A099198 A365988

Adjacent sequences: A041368 A041369 A041370 * A041372 A041373 A041374

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved