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A041159
Denominators of continued fraction convergents to sqrt(89).
2
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
0,2
LINKS
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
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved