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 A041008 Numerators of continued fraction convergents to sqrt(7). 6

%I

%S 2,3,5,8,37,45,82,127,590,717,1307,2024,9403,11427,20830,32257,149858,

%T 182115,331973,514088,2388325,2902413,5290738,8193151,38063342,

%U 46256493,84319835,130576328,606625147

%N Numerators of continued fraction convergents to sqrt(7).

%H Vincenzo Librandi, <a href="/A041008/b041008.txt">Table of n, a(n) for n = 0..200</a>

%H C. Elsner, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Elsner/elsner9.html">Series of Error Terms for Rational Approximations of Irrational Numbers </a>, J. Int. Seq. 14 (2011) # 11.1.4

%H C. Elsner, M. Stein, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Elsner2/elsner10.html">On Error Sum Functions Formed by Convergents of Real Numbers</a>, J. Int. Seq. 14 (2011) # 11.8.6

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,16,0,0,0,-1).

%F G.f.: (2+3*x+5*x^2+8*x^3+5*x^4-3*x^5+2*x^6-x^7)/(1-16*x^4+x^8)

%t Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[7],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 16 2011*)

%t Numerator[Convergents[Sqrt[7], 30]] (* _Vincenzo Librandi_, Oct 28 2013 *)