A041206 - OEIS

%I #15 Nov 30 2024 18:03:00

%S 10,11,32,331,694,1025,21194,22219,65632,678539,1422710,2101249,

%T 43447690,45548939,134545568,1391004619,2916554806,4307559425,

%U 89067743306,93375302731,275818348768,2851558790411

%N Numerators of continued fraction convergents to sqrt(114).

%H Vincenzo Librandi, <a href="/A041206/b041206.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 (0,0,0,0,0,2050,0,0,0,0,0,-1).

%F a(n) = 2050*a(n-6)-a(n-12). G.f.: -(x^11-10*x^10+11*x^9-32*x^8+331*x^7-694*x^6-1025*x^5-694*x^4-331*x^3-32*x^2-11*x-10)/(x^12-2050*x^6+1). [_Colin Barker_, Jul 19 2012]

%t Numerator[Convergents[Sqrt[114], 30]] (* _Vincenzo Librandi_, Oct 26 2013 *)

%t LinearRecurrence[{0,0,0,0,0,2050,0,0,0,0,0,-1},{10,11,32,331,694,1025,21194,22219,65632,678539,1422710,2101249},30] (* _Harvey P. Dale_, Nov 30 2024 *)

%Y Cf. A041207.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.