A041773 Denominators of continued fraction convergents to sqrt(407).

1, 5, 6, 17, 23, 132, 5303, 26647, 31950, 90547, 122497, 703032, 28243777, 141921917, 170165694, 482253305, 652418999, 3744348300, 150426350999, 755876103295, 906302454294, 2568481011883, 3474783466177, 19942398342768, 801170717176897, 4025795984227253

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, 5326, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10-5*x^9+6*x^8-17*x^7+23*x^6-132*x^5-23*x^4-17*x^3-6*x^2-5*x-1) / (x^12-5326*x^6+1). - Colin Barker, Nov 24 2013

a(n) = 5326*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 24 2013

Mathematica

Denominator[Convergents[Sqrt[407], 40]] (* Harvey P. Dale, Jul 13 2012 *)
CoefficientList[Series[-(x^10 - 5 x^9 + 6 x^8 - 17 x^7 + 23 x^6 - 132 x^5 - 23 x^4 - 17 x^3 - 6 x^2 - 5 x - 1)/(x^12 - 5326 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 24 2013 *)

Prog

(Magma) I:=[1, 5, 6, 17, 23, 132, 5303, 26647, 31950, 90547, 122497, 703032]; [n le 12 select I[n] else 5326*Self(n-6)-Self(n-12): n in [1..50]]; // Vincenzo Librandi, Dec 24 2013

Crossrefs

Cf. A041772, A040386.

Sequence in context: A035595 A099571 A041997 * A041054 A297980 A120034

Adjacent sequences: A041770 A041771 A041772 * A041774 A041775 A041776

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved