A041785 Denominators of continued fraction convergents to sqrt(413).

1, 3, 28, 31, 152, 183, 1799, 5580, 224999, 680577, 6350192, 7030769, 34473268, 41504037, 408009601, 1265532840, 51029323201, 154353502443, 1440210845188, 1594564347631, 7818468235712, 9413032583343, 92535761485799, 287020317040740, 11573348443115399

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, 0, 0, 0, 0, 0, 0, 226798, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -3*x^13 +28*x^12 -31*x^11 +152*x^10 -183*x^9 +1799*x^8 -5580*x^7 -1799*x^6 -183*x^5 -152*x^4 -31*x^3 -28*x^2 -3*x -1) / (x^16 -226798*x^8 +1). - Colin Barker, Nov 24 2013

a(n) = 226798*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 24 2013

Mathematica

Denominator[Convergents[Sqrt[413], 30]] (* Vincenzo Librandi, Dec 24 2013 *)

Prog

(Magma) I:=[1, 3, 28, 31, 152, 183, 1799, 5580, 224999, 680577, 6350192, 7030769, 34473268, 41504037, 408009601, 1265532840]; [n le 16 select I[n] else 226798*Self(n-8)-Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 24 2013

Crossrefs

Cf. A041784, A040392.

Sequence in context: A224579 A037102 A042169 * A157848 A225674 A253653

Adjacent sequences: A041782 A041783 A041784 * A041786 A041787 A041788

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 24 2013

Status

approved