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
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).
Programs
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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
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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 *)
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
Extensions
More terms from Colin Barker, Nov 14 2013