A041098 - OEIS

%I #17 Jul 22 2016 11:01:06

%S 7,8,15,68,83,151,2197,2348,4545,20528,25073,45601,663487,709088,

%T 1372575,6199388,7571963,13771351,200370877,214142228,414513105,

%U 1872194648,2286707753,4158902401,60511341367

%N Numerators of continued fraction convergents to sqrt(57).

%H Vincenzo Librandi, <a href="/A041098/b041098.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 (0,0,0,0,0,302,0,0,0,0,0,-1).

%F a(n) = 302*a(n-6)-a(n-12). G.f.: -(x^11-7*x^10+8*x^9-15*x^8+68*x^7-83*x^6-151*x^5-83*x^4-68*x^3-15*x^2-8*x-7)/(x^12-302*x^6+1). [_Colin Barker_, Jul 18 2012]

%t Numerator[Convergents[Sqrt[57], 30]] (* _Vincenzo Librandi_, Oct 25 2013 *)

%t LinearRecurrence[{0,0,0,0,0,302,0,0,0,0,0,-1},{7,8,15,68,83,151,2197,2348,4545,20528,25073,45601},30] (* _Harvey P. Dale_, Jul 22 2016 *)

%Y Cf. A010510, A041099.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.