A041454 - OEIS

%I #14 Aug 10 2021 18:49:32

%S 15,16,31,78,265,4053,12424,28901,41325,70226,2148105,2218331,4366436,

%T 10951203,37220045,569251878,1744975679,4059203236,5804178915,

%U 9863382151,301705643445,311569025596,613274669041,1538118363678,5227629760075,79952564764803

%N Numerators of continued fraction convergents to sqrt(243).

%H Vincenzo Librandi, <a href="/A041454/b041454.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 (0,0,0,0,0,0,0,0,0,140452,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^19 -15*x^18 +16*x^17 -31*x^16 +78*x^15 -265*x^14 +4053*x^13 -12424*x^12 +28901*x^11 -41325*x^10 -70226*x^9 -41325*x^8 -28901*x^7 -12424*x^6 -4053*x^5 -265*x^4 -78*x^3 -31*x^2 -16*x -15) / (x^20 -140452*x^10 +1). - _Colin Barker_, Nov 10 2013

%t Numerator[Convergents[Sqrt[243], 30]] (* _Vincenzo Librandi_, Nov 02 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,140452,0,0,0,0,0,0,0,0,0,-1},{15,16,31,78,265,4053,12424,28901,41325,70226,2148105,2218331,4366436,10951203,37220045,569251878,1744975679,4059203236,5804178915,9863382151},40] (* _Harvey P. Dale_, Aug 10 2021 *)

%Y Cf. A041455.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 10 2013