A041163 Denominators of continued fraction convergents to sqrt(91).

1, 1, 2, 11, 13, 76, 89, 165, 3059, 3224, 6283, 34639, 40922, 239249, 280171, 519420, 9629731, 10149151, 19778882, 109043561, 128822443, 753155776, 881978219, 1635133995, 30314390129, 31949524124, 62263914253, 343269095389, 405533009642, 2370934143599

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,3148,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -x^13 +2*x^12 -11*x^11 +13*x^10 -76*x^9 +89*x^8 -165*x^7 -89*x^6 -76*x^5 -13*x^4 -11*x^3 -2*x^2 -x -1) / (x^16 -3148*x^8 +1). - Colin Barker, Nov 14 2013

a(n) = 3148*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 12 2013

Mathematica

Denominator[Convergents[Sqrt[91], 30]] (* Bruno Berselli, Nov 14 2013 *)
CoefficientList[Series[-(x^14 - x^13 + 2 x^12 - 11 x^11 + 13 x^10 - 76 x^9 + 89 x^8 - 165 x^7 - 89 x^6 - 76 x^5 - 13 x^4 - 11 x^3 - 2 x^2 - x - 1)/(x^16 - 3148 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)

Prog

(Magma) I:=[1, 1, 2, 11, 13, 76, 89, 165, 3059, 3224, 6283, 34639, 40922, 239249, 280171, 519420]; [n le 16 select I[n] else 3148*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Crossrefs

Cf. A041162, A010162, A020848, A010542.

Sequence in context: A262832 A091021 A042563 * A073914 A266991 A041971

Adjacent sequences: A041160 A041161 A041162 * A041164 A041165 A041166

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved