%I #21 Jul 09 2025 01:25:10

%S 20,61,81,142,223,4379,4602,8981,13583,49730,2002783,6058079,8060862,

%T 14118941,22179803,435535198,457715001,893250199,1350965200,

%U 4946145799,199196797160,602536537279,801733334439,1404269871718,2206003206157,43318330788701

%N Numerators of continued fraction convergents to sqrt(411).

%H Vincenzo Librandi, <a href="/A041780/b041780.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 (0,0,0,0,0,0,0,0,0,99460,0,0,0,0,0,0,0,0,0,-1).

%F a(n) = 99460*a(n-10)-a(n-20). - _Vincenzo Librandi_, Nov 08 2013

%F G.f.: -(x^19 -20*x^18 +61*x^17 -81*x^16 +142*x^15 -223*x^14 +4379*x^13 -4602*x^12 +8981*x^11 -13583*x^10 -49730*x^9 -13583*x^8 -8981*x^7 -4602*x^6 -4379*x^5 -223*x^4 -142*x^3 -81*x^2 -61*x -20) / (x^20 -99460*x^10 +1). - _Colin Barker_, Dec 28 2013

%t Numerator[Convergents[Sqrt[411], 30]] (* _Vincenzo Librandi_, Nov 08 2013 *)

%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 99460, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {20, 61, 81, 142, 223, 4379, 4602, 8981, 13583, 49730, 2002783, 6058079, 8060862, 14118941, 22179803, 435535198, 457715001, 893250199, 1350965200, 4946145799}, 30] (* _Vincenzo Librandi_, Nov 08 2013 *)

%o (Magma) I:=[20,61,81,142,223,4379,4602,8981,13583,49730, 2002783,6058079,8060862,14118941,22179803,435535198, 457715001,893250199,1350965200,4946145799]; [n le 20 select I[n] else 99460*Self(n-10)-Self(n-20): n in [1..30]]; // _Vincenzo Librandi_, Nov 08 2013

%Y Cf. A041781, A040390.

%K nonn,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Dec 28 2013