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%I #19 Sep 08 2022 08:44:54
%S 1,3,4,15,19,34,53,87,314,401,1517,45911,139250,185161,694733,879894,
%T 1574627,2454521,4029148,14541965,18571113,70255304,2126230233,
%U 6448946003,8575176236,32174474711,40749650947,72924125658,113673776605,186597902263,673467483394
%N Denominators of continued fraction convergents to sqrt(233).
%H Vincenzo Librandi, <a href="/A041435/b041435.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F G.f.: -(x^20 -3*x^19 +4*x^18 -15*x^17 +19*x^16 -34*x^15 +53*x^14 -87*x^13 +314*x^12 -401*x^11 +1517*x^10 +401*x^9 +314*x^8 +87*x^7 +53*x^6 +34*x^5 +19*x^4 +15*x^3 +4*x^2 +3*x +1) / (x^22 +46312*x^11 -1). - _Colin Barker_, Nov 17 2013
%F a(n) = 46312*a(n-11) + a(n-22) for n>21. - _Vincenzo Librandi_, Dec 17 2013
%t Denominator[Convergents[Sqrt[233], 30]] (* _Vincenzo Librandi_, Dec 17 2013 *)
%o (Magma) I:=[1,3,4,15,19,34,53,87,314,401,1517,45911, 139250,185161,694733,879894,1574627,2454521,4029148, 14541965,18571113,70255304]; [n le 22 select I[n] else 46312*Self(n-11)+Self(n-22): n in [1..40]]; // _Vincenzo Librandi_, Dec 17 2013
%Y Cf. A041434, A040217.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 17 2013