A041633 Denominators of continued fraction convergents to sqrt(335).

1, 3, 10, 33, 1198, 3627, 12079, 39864, 1447183, 4381413, 14591422, 48155679, 1748195866, 5292743277, 17626425697, 58172020368, 2111819158945, 6393629497203, 21292707650554, 70271752448865, 2551075795809694, 7723499139877947, 25721573215443535

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, 1208, 0, 0, 0, -1).

Formula

G.f.: -(x^2-3*x-1)*(x^4+11*x^2+1) / (x^8-1208*x^4+1). - Colin Barker, Nov 20 2013

a(n) = 1208*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[335], 30]] (* Vincenzo Librandi, Dec 22 2013 *)
LinearRecurrence[{0, 0, 0, 1208, 0, 0, 0, -1}, {1, 3, 10, 33, 1198, 3627, 12079, 39864}, 30] (* Harvey P. Dale, Aug 11 2019 *)

Prog

(Magma) I:=[1, 3, 10, 33, 1198, 3627, 12079, 39864]; [n le 8 select I[n] else 1208*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041632, A040316.

Sequence in context: A149031 A145928 A006535 * A308499 A034215 A193036

Adjacent sequences: A041630 A041631 A041632 * A041634 A041635 A041636

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 20 2013

Status

approved