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A041119

Denominators of continued fraction convergents to sqrt(68).

1, 4, 65, 264, 4289, 17420, 283009, 1149456, 18674305, 75846676, 1232221121, 5004731160, 81307919681, 330236409884, 5365090477825, 21790598321184, 354014663616769, 1437849252788260, 23359602708228929, 94876260085703976, 1541379764079492545

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OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,66,0,-1).

FORMULA

G.f.: -(x^2-4*x-1) / ((x^2-8*x-1)*(x^2+8*x-1)). - Colin Barker, Nov 13 2013

a(n) = 66*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 11 2013

MATHEMATICA

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[68], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)

Denominator[Convergents[Sqrt[68], 30]] (* Vincenzo Librandi, Dec 11 2013 *)

PROG

(Magma) I:=[1, 4, 65, 264]; [n le 4 select I[n] else 66*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013

CROSSREFS

Cf. A041118, A040059, A020825, A010520.

Sequence in context: A119601 A058438 A171959 * A278547 A293562 A382443

Adjacent sequences: A041116 A041117 A041118 * A041120 A041121 A041122

KEYWORD

nonn,cofr,easy,frac

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Colin Barker, Nov 13 2013

STATUS

approved

URL: https://oeis.org/A041119

⇱ A041119 - OEIS