A042393 Denominators of continued fraction convergents to sqrt(723).

1, 1, 8, 9, 476, 485, 3871, 4356, 230383, 234739, 1873556, 2108295, 111504896, 113613191, 906797233, 1020410424, 53968139281, 54988549705, 438887987216, 493876536921, 26120467907108, 26614344444029, 212420879015311, 239035223459340, 12642252498900991

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 484, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+9*x^2+1) / (x^8-484*x^4+1). - Colin Barker, Dec 10 2013

Mathematica

Denominator[Convergents[Sqrt[723], 30]] (* Harvey P. Dale, May 01 2013 *)
CoefficientList[Series[(1 + x - x^2) (x^4 + 9 x^2 + 1)/(x^8 - 484 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 21 2014 *)

Prog

(Magma) I:=[1, 1, 8, 9, 476, 485, 3871, 4356]; [n le 8 select I[n] else 484*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Jan 21 2014

Crossrefs

Cf. A042392, A040696.

Sequence in context: A239524 A115073 A298020 * A264777 A114132 A038704

Adjacent sequences: A042390 A042391 A042392 * A042394 A042395 A042396

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 10 2013

Status

approved