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%I #30 Jul 14 2015 16:51:01
%S 3,4,27,31,213,244,1677,1921,13203,15124,103947,119071,818373,937444,
%T 6443037,7380481,50725923,58106404,399364347,457470751,3144188853,
%U 3601659604,24754146477,28355806081
%N Numerators of continued fraction convergents to sqrt(15).
%H Vincenzo Librandi, <a href="/A041022/b041022.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-1).
%F G.f.: (3+4*x+3*x^2-x^3)/(1-8*x^2+x^4).
%F From _Gerry Martens_, Jul 11 2015: (Start)
%F Interspersion of 2 sequences [a0(n),a1(n)] for n>0:
%F a0(n) = (-((4-sqrt(15))^n*(3+sqrt(15)))+(-3+sqrt(15))*(4+sqrt(15))^n)/2.
%F a1(n) = ((4-sqrt(15))^n+(4+sqrt(15))^n)/2. (End)
%t Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[15],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 17 2011 *)
%t Numerator[Convergents[Sqrt[15], 30]] (* _Vincenzo Librandi_, Oct 28 2013 *)
%t a0[n_] := (-((4-Sqrt[15])^n*(3+Sqrt[15]))+(-3+Sqrt[15])*(4+Sqrt[15])^n)/2 // Simplify
%t a1[n_] := ((4-Sqrt[15])^n+(4+Sqrt[15])^n)/2 // Simplify
%t Flatten[MapIndexed[{a0[#], a1[#]} &,Range[20]]] (* _Gerry Martens_, Jul 11 2015 *)
%Y Cf. A010472, A041023.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_
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