A041212 - OEIS

%I #18 May 09 2021 20:59:19

%S 10,11,54,119,530,649,13510,14159,70146,154451,687950,842401,17535970,

%T 18378371,91049454,200477279,892958570,1093435849,22761675550,

%U 23855111399,118182121146,260219353691,1159059535910

%N Numerators of continued fraction convergents to sqrt(117).

%H Vincenzo Librandi, <a href="/A041212/b041212.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 (0,0,0,0,0,1298,0,0,0,0,0,-1).

%F From _Colin Barker_, Jul 19 2012: (Start)

%F a(n) = 1298*a(n-6) - a(n-12).

%F G.f.: -(x^11 - 10*x^10 + 11*x^9 - 54*x^8 + 119*x^7 - 530*x^6 - 649*x^5 - 530*x^4 - 119*x^3 - 54*x^2 - 11*x - 10)/((x^2 - 3*x - 1)*(x^2 + 3*x - 1)*(x^4 - 3*x^3 + 10*x^2 + 3*x + 1)*(x^4 + 3*x^3 + 10*x^2 - 3*x + 1)). (End)

%t Numerator[Convergents[Sqrt[117], 30]] (* _Vincenzo Librandi_, Oct 26 2013 *)

%Y Cf. A010182, A041213.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_