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Denominators of continued fraction convergents to sqrt(816).
2

%I #20 Sep 08 2022 08:44:55

%S 1,1,2,7,23,76,99,175,9899,10074,19973,69993,229952,759849,989801,

%T 1749650,98970201,100719851,199690052,699790007,2299060073,7596970226,

%U 9896030299,17493000525,989504059699,1006997060224,1996501119923,6996500419993,22986002379902

%N Denominators of continued fraction convergents to sqrt(816).

%H Vincenzo Librandi, <a href="/A042575/b042575.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 (0,0,0,0,0,0,0,9998,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^14 -x^13 +2*x^12 -7*x^11 +23*x^10 -76*x^9 +99*x^8 -175*x^7 -99*x^6 -76*x^5 -23*x^4 -7*x^3 -2*x^2 -x -1) / ((x^8 -100*x^4 +1)*(x^8 +100*x^4 +1)). - _Colin Barker_, Dec 18 2013

%F a(n) = 9998*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Jan 25 2014

%t Denominator/@Convergents[Sqrt[816], 30] (* _Harvey P. Dale_, Jun 14 2011 *)

%o (Magma) I:=[1,1,2,7,23,76,99,175,9899,10074,19973,69993, 229952,759849,989801,1749650]; [n le 16 select I[n] else 9998*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Jan 25 2014

%Y Cf. A042574, A040787.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 18 2013