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%I #18 Sep 08 2022 08:45:38
%S 1,1,17,35,577,1189,19601,40391,665857,1372105,22619537,46611179,
%T 768398401,1583407981,26102926097,53789260175,886731088897,
%U 1827251437969,30122754096401,62072759630771,1023286908188737,2108646576008245,34761632124320657,71631910824649559
%N Denominators of continued fraction convergents to sqrt(8/9).
%H Vincenzo Librandi, <a href="/A144534/b144534.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,34,0,-1).
%F a(n) = 16*a(n-1) + a(n-2) if n odd, otherwise a(n) = 2*a(n-1) + a(n-2), for n >= 2.
%F a(n) = 34*a(n-2)-a(n-4). G.f.: (x^3-17*x^2+x+1)/((x^2-6*x+1)*(x^2+6*x+1)). [_Colin Barker_, Jul 16 2012]
%e 0, 1, 16/17, 33/35, 544/577, 1121/1189, 18480/19601, 38081/40391, 627776/665857, ...
%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[8/9], n]]], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 23 2011 *)
%t Denominator[Convergents [Sqrt[8/9], 30]] (* _Vincenzo Librandi_, Feb 01 2014 *)
%o (Magma) I:=[1,1,17,35]; [n le 4 select I[n] else 34*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Feb 01 2014
%Y Cf. A040000, A144532, A144533.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 29 2008
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