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Denominators of continued fraction convergents to sqrt(936).
2

%I #19 Sep 08 2022 08:44:55

%S 1,1,2,5,32,69,101,170,10301,10471,20772,52015,332862,717739,1050601,

%T 1768340,107151001,108919341,216070342,541060025,3462430492,

%U 7465921009,10928351501,18394272510,1114584702101,1132978974611,2247563676712,5628106328035

%N Denominators of continued fraction convergents to sqrt(936).

%H Vincenzo Librandi, <a href="/A042811/b042811.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_16">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 -x^13 +2*x^12 -5*x^11 +32*x^10 -69*x^9 +101*x^8 -170*x^7 -101*x^6 -69*x^5 -32*x^4 -5*x^3 -2*x^2 -x -1) / ((x^4 -10*x^2 -1)*(x^4 +10*x^2 -1)*(x^8 +102*x^4 +1)). - _Colin Barker_, Dec 23 2013

%F a(n) = 10402*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Jan 30 2014

%t Denominator/@Convergents[Sqrt[936], 30] (* _Harvey P. Dale_, Apr 18 2011 *)

%o (Magma) I:=[1,1,2,5,32,69,101,170,10301,10471,20772, 52015,332862,717739,1050601,1768340]; [n le 16 select I[n] else 10402*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Jan 30 2014

%Y Cf. A042810, A040905.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 23 2013