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Denominators of continued fraction convergents to sqrt(316).
2

%I #17 Sep 08 2022 08:44:54

%S 1,1,4,9,76,161,559,720,25039,25759,102316,230391,1945444,4121279,

%T 14309281,18430560,640948321,659378881,2619084964,5897548809,

%U 49799475436,105496499681,366288974479,471785474160,16406995095919,16878780570079,67043336806156

%N Denominators of continued fraction convergents to sqrt(316).

%H Vincenzo Librandi, <a href="/A041597/b041597.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 (0,0,0,0,0,0,0,25598,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^14 -x^13 +4*x^12 -9*x^11 +76*x^10 -161*x^9 +559*x^8 -720*x^7 -559*x^6 -161*x^5 -76*x^4 -9*x^3 -4*x^2 -x -1) / ((x^8 -160*x^4 +1)*(x^8 +160*x^4 +1)). - _Colin Barker_, Nov 19 2013

%F a(n) = 25598*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 21 2013

%t Denominator[Convergents[Sqrt[316], 30]] (* _Vincenzo Librandi_ Dec 21 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,25598,0,0,0,0,0,0,0,-1},{1,1,4,9,76,161,559,720,25039,25759,102316,230391,1945444,4121279,14309281,18430560},30] (* _Harvey P. Dale_, Mar 21 2017 *)

%o (Magma) I:=[1,1,4,9,76,161,559,720,25039,25759,102316, 230391,1945444,4121279,14309281,18430560]; [n le 16 select I[n] else 25598*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 21 2013

%Y Cf. A041596, A040298.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 19 2013