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%I #18 Sep 08 2022 08:44:54
%S 1,2,3,5,48,53,101,255,10301,20857,31158,52015,499293,551308,1050601,
%T 2652510,107151001,216954512,324105513,541060025,5193645738,
%U 5734705763,10928351501,27591408765,1114584702101,2256760812967,3371345515068,5628106328035
%N Denominators of continued fraction convergents to sqrt(416).
%H Vincenzo Librandi, <a href="/A041791/b041791.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 (0,0,0,0,0,0,0,10402,0,0,0,0,0,0,0,-1).
%F G.f.: -(x^14 -2*x^13 +3*x^12 -5*x^11 +48*x^10 -53*x^9 +101*x^8 -255*x^7 -101*x^6 -53*x^5 -48*x^4 -5*x^3 -3*x^2 -2*x -1) / ((x^4 -10*x^2 -1)*(x^4 +10*x^2 -1)*(x^8 +102*x^4 +1)). - _Colin Barker_, Nov 24 2013
%F a(n) = 10402*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 24 2013
%t Denominator[Convergents[Sqrt[416], 30]] (* _Vincenzo Librandi_, Dec 24 2013 *)
%t LinearRecurrence[{0,0,0,0,0,0,0,10402,0,0,0,0,0,0,0,-1},{1,2,3,5,48,53,101,255,10301,20857,31158,52015,499293,551308,1050601,2652510},30] (* _Harvey P. Dale_, Feb 15 2016 *)
%o (Magma) I:=[1,2,3,5,48,53,101,255,10301,20857,31158, 52015,499293,551308,1050601,2652510]; [n le 16 select I[n] else 10402*Self(n-8)-Self(n-16): n in [1..50]]; // _Vincenzo Librandi_, Dec 24 2013
%Y Cf. A041790, A040395.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 24 2013
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