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Denominators of continued fraction convergents to sqrt(761).
2

%I #22 Jun 27 2022 01:48:51

%S 1,1,2,5,12,17,29,1583,1612,3195,8002,19199,27201,46400,2532801,

%T 2579201,5112002,12803205,30718412,43521617,74240029,4052483183,

%U 4126723212,8179206395,20485136002,49149478399,69634614401,118784092800,6483975625601,6602759718401

%N Denominators of continued fraction convergents to sqrt(761).

%H Vincenzo Librandi, <a href="/A042467/b042467.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,1600,0,0,0,0,0,0,1).

%F G.f.: -(x^12 - x^11 + 2*x^10 - 5*x^9 + 12*x^8 - 17*x^7 + 29*x^6 + 17*x^5 + 12*x^4 + 5*x^3 + 2*x^2 + x + 1) / (x^14 + 1600*x^7 - 1). - _Colin Barker_, Dec 14 2013

%F a(n) = 1600*a(n-7) + a(n-14). - _Vincenzo Librandi_, Dec 14 2013

%t Denominator[Convergents[Sqrt[761], 30]] (* _Vincenzo Librandi_, Dec 14 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,1600,0,0,0,0,0,0,1},{1,1,2,5,12,17,29,1583,1612,3195,8002,19199,27201,46400},30] (* _Harvey P. Dale_, Aug 23 2015 *)

%o (Magma) I:=[1,1,2,5,12,17,29,1583,1612,3195,8002,19199, 27201,46400]; [n le 14 select I[n] else 1600*Self(n-7)+Self(n-14): n in [1..40]]; // _Vincenzo Librandi_, Dec 14 2013

%Y Cf. A042466, A040733.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Dec 14 2013