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Denominators of continued fraction convergents to sqrt(567).
2

%I #22 Nov 24 2022 14:45:32

%S 1,1,5,16,69,85,3979,4064,20235,64769,279311,344080,16106991,16451071,

%T 81911275,262184896,1130650859,1392835755,65201095589,66593931344,

%U 331576820965,1061324394239,4576874397921,5638198792160,263934018837281,269572217629441

%N Denominators of continued fraction convergents to sqrt(567).

%H Vincenzo Librandi, <a href="/A042087/b042087.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,4048,0,0,0,0,0,-1).

%F G.f.: -(x^10 -x^9 +5*x^8 -16*x^7 +69*x^6 -85*x^5 -69*x^4 -16*x^3 -5*x^2 -x -1) / ((x^4 -16*x^2 +1)*(x^8 +16*x^6 +255*x^4 +16*x^2 +1)). - _Colin Barker_, Dec 01 2013

%F a(n) = 4048*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Jan 14 2014

%t Denominator[Convergents[Sqrt[567], 30]] (* _Vincenzo Librandi_, Jan 14 2014 *)

%t LinearRecurrence[{0,0,0,0,0,4048,0,0,0,0,0,-1},{1,1,5,16,69,85,3979,4064,20235,64769,279311,344080},40] (* _Harvey P. Dale_, Nov 24 2022 *)

%o (Magma) I:=[1,1,5,16,69,85,3979,4064,20235,64769,279311, 344080]; [n le 12 select I[n] else 4048*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Jan 14 2014

%Y Cf. A042086, A040543.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Dec 01 2013