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%I #15 Oct 09 2022 14:31:41
%S 0,1,16,33,544,1121,18480,38081,627776,1293633,21325904,43945441,
%T 724452960,1492851361,24610074736,50713000833,836018088064,
%U 1722749176961,28400004919440,58522759015841,964764149172896,1988051057361633,32773581066959024,67535213191279681
%N Numerators of continued fraction convergents to sqrt(8/9).
%H Vincenzo Librandi, <a href="/A144533/b144533.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*(x^2-16*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 CoefficientList[Series[- x (x^2 - 16 x - 1)/((x^2 - 6 x + 1) (x^2 + 6 x + 1)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 10 2013 *)
%t Convergents[Sqrt[8/9],30]//Numerator (* or *) LinearRecurrence[{0,34,0,-1},{0,1,16,33},30] (* _Harvey P. Dale_, Oct 09 2022 *)
%o (Magma) I:=[0, 1, 16, 33]; [n le 4 select I[n] else 34*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 10 2013
%Y Cf. A040000, A144532, A144534.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 29 2008
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