A041978 - OEIS

%I #19 Jun 13 2015 00:49:38

%S 22,23,45,68,181,1154,12875,78404,169683,248087,417770,665857,

%T 29715478,30381335,60096813,90478148,241053109,1536796802,17145817931,

%U 104411704388,225969226707,330380931095,556350157802,886731088897,39572518069270,40459249158167

%N Numerators of continued fraction convergents to sqrt(512).

%H Vincenzo Librandi, <a href="/A041978/b041978.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 (0,0,0,0,0,0,0,0,0,0,0,1331714,0,0,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^23 -22*x^22 +23*x^21 -45*x^20 +68*x^19 -181*x^18 +1154*x^17 -12875*x^16 +78404*x^15 -169683*x^14 +248087*x^13 -417770*x^12 -665857*x^11 -417770*x^10 -248087*x^9 -169683*x^8 -78404*x^7 -12875*x^6 -1154*x^5 -181*x^4 -68*x^3 -45*x^2 -23*x -22) / ((x^6 -34*x^3 +1)*(x^6 +34*x^3 +1)*(x^12 +1154*x^6 +1)). - _Colin Barker_, Nov 28 2013

%F Limit n->infinity a(n)^(1/n) = (1+sqrt(2))^(4/3) = 3.2386765777... - _Vaclav Kotesovec_, Nov 28 2013

%t Numerator[Convergents[Sqrt[512], 30]] (* _Harvey P. Dale_, Apr 09 2012 *)

%Y Cf. A041979, A040489.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 28 2013