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%I #15 Sep 08 2022 08:44:54
%S 1,1,5,41,46,133,312,445,3872,15933,19805,689303,709108,3525735,
%T 28914988,32440723,93796434,220033591,313830025,2730673791,
%U 11236525189,13967198980,486121290509,500088489489,2486475248465,20391890477209,22878365725674,66148621928557
%N Denominators of continued fraction convergents to sqrt(317).
%H Vincenzo Librandi, <a href="/A041599/b041599.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 (0,0,0,0,0,0,0,0,0,0,705236,0,0,0,0,0,0,0,0,0,0,1).
%F G.f.: -(x^20 -x^19 +5*x^18 -41*x^17 +46*x^16 -133*x^15 +312*x^14 -445*x^13 +3872*x^12 -15933*x^11 +19805*x^10 +15933*x^9 +3872*x^8 +445*x^7 +312*x^6 +133*x^5 +46*x^4 +41*x^3 +5*x^2 +x +1) / (x^22 +705236*x^11 -1). - _Colin Barker_, Nov 19 2013
%F a(n) = 705236*a(n-11) + a(n-22) for n>21. - _Vincenzo Librandi_, Dec 21 2013
%t Denominator[Convergents[Sqrt[317], 30]] (* _Vincenzo Librandi_ Dec 21 2013 *)
%o (Magma) I:=[1,1,5,41,46,133,312,445,3872,15933,19805, 689303,709108,3525735,28914988,32440723,93796434, 220033591,313830025,2730673791,11236525189, 13967198980]; [n le 22 select I[n] else 705236*Self(n-11)+Self(n-22): n in [1..40]]; // _Vincenzo Librandi_, Dec 21 2013
%Y Cf. A041598, A040299.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 19 2013
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