A041881 Denominators of continued fraction convergents to sqrt(462).

1, 2, 85, 172, 7309, 14790, 628489, 1271768, 54042745, 109357258, 4647047581, 9403452420, 399592049221, 808587550862, 34360269185425, 69529125921712, 2954583557897329, 5978696241716370, 254059825709984869, 514098347661686108, 21846190427500801405

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,86,0,-1).

Formula

G.f.: -(x^2 -2*x -1) / (x^4 -86*x^2 +1). - Colin Barker, Nov 26 2013

a(n) = 86*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[462], 30]] (* Harvey P. Dale, Sep 30 2011 *)
CoefficientList[Series[(1 + 2 x - x^2)/(x^4 - 86 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(Magma) I:=[1, 2, 85, 172]; [n le 4 select I[n] else 86*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041880, A040440.

Sequence in context: A244947 A078166 A101578 * A076542 A226842 A303892

Adjacent sequences: A041878 A041879 A041880 * A041882 A041883 A041884

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 26 2013

Status

approved