A041159 Denominators of continued fraction convergents to sqrt(89).
1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000, 977001, 2007002, 6998007, 23001023, 53000053, 977001977, 2007004007, 6998013998, 23001046001, 53000106000, 977002954001, 2007006014002, 6998020996007, 23001069002023, 53000159000053, 977003931002977
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1000,0,0,0,0,1).
Programs
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Magma
I:=[1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000]; [n le 10 select I[n] else 1000*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013
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Mathematica
Denominator/@Convergents[Sqrt[89], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *) CoefficientList[Series[-(x^8 - 2 x^7 + 7 x^6 - 23 x^5 + 53 x^4 + 23 x^3 + 7 x^2 + 2 x + 1)/(x^10 + 1000 x^5 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *) LinearRecurrence[{0,0,0,0,1000,0,0,0,0,1},{1,2,7,23,53,977,2007,6998,23001,53000},30] (* Harvey P. Dale, Feb 07 2019 *)
Formula
G.f.: -(x^8-2*x^7+7*x^6-23*x^5+53*x^4+23*x^3+7*x^2+2*x+1) / (x^10+1000*x^5-1). - Colin Barker, Nov 14 2013
a(n) = 1000*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 12 2013