A041123 Denominators of continued fraction convergents to sqrt(70).
1, 2, 3, 8, 11, 30, 491, 1012, 1503, 4018, 5521, 15060, 246481, 508022, 754503, 2017028, 2771531, 7560090, 123732971, 255026032, 378759003, 1012544038, 1391303041, 3795150120, 62113704961, 128022560042
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,502,0,0,0,0,0,-1).
Programs
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Mathematica
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[70],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *) Denominator[Convergents[Sqrt[70], 30]] (* Vincenzo Librandi, Oct 24 2013 *)
Formula
a(n) = 502*a(n-6)-a(n-12). G.f.: -(x^2-2*x-1)*(x^8+4*x^6+15*x^4+4*x^2+1)/ (x^12-502*x^6+1). [Colin Barker, Jul 18 2012]