A041575 Denominators of continued fraction convergents to sqrt(305).

1, 2, 13, 28, 965, 1958, 12713, 27384, 943769, 1914922, 12433301, 26781524, 923005117, 1872791758, 12159755665, 26192303088, 902698060657, 1831588424402, 11892228607069, 25616045638540, 882837780317429, 1791291606273398, 11630587417957817, 25052466442189032

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,978,0,0,0,-1).

Formula

G.f.: -(x^2-2*x-1)*(x^4+14*x^2+1) / (x^8-978*x^4+1). - Colin Barker, Nov 19 2013

a(n) = 978*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[305], 30]] (* Vincenzo Librandi, Dec 20 2013 *)
LinearRecurrence[{0, 0, 0, 978, 0, 0, 0, -1}, {1, 2, 13, 28, 965, 1958, 12713, 27384}, 30] (* Harvey P. Dale, Nov 03 2015 *)

Prog

(Magma) I:=[1, 2, 13, 28, 965, 1958, 12713, 27384]; [n le 8 select I[n] else 978*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041574, A040287.

Sequence in context: A294559 A041017 A033837 * A042917 A366720 A174049

Adjacent sequences: A041572 A041573 A041574 * A041576 A041577 A041578

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved