A042673 Denominators of continued fraction convergents to sqrt(866).

1, 2, 5, 7, 201, 208, 617, 1442, 84253, 169948, 424149, 594097, 17058865, 17652962, 52364789, 122382540, 7150552109, 14423486758, 35997525625, 50421012383, 1447785872349, 1498206884732, 4444199641813, 10386606168358, 606867357406577, 1224121320981512

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, 84870, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -2*x^13 +5*x^12 -7*x^11 +201*x^10 -208*x^9 +617*x^8 -1442*x^7 -617*x^6 -208*x^5 -201*x^4 -7*x^3 -5*x^2 -2*x -1) / (x^16 -84870*x^8 +1). - Colin Barker, Dec 20 2013

a(n) = 84870*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[866], 30]] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 2, 5, 7, 201, 208, 617, 1442, 84253, 169948, 424149, 594097, 17058865, 17652962, 52364789, 122382540]; [n le 16 select I[n] else 84870*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A042672, A040836.

Sequence in context: A242169 A058854 A006275 * A214705 A252283 A007571

Adjacent sequences: A042670 A042671 A042672 * A042674 A042675 A042676

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 20 2013

Status

approved