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%I #23 Jul 14 2015 16:53:36
%S 15,31,945,1921,58575,119071,3630705,7380481,225045135,457470751,
%T 13949167665,28355806081,864623350095,1757602506271,53592698538225,
%U 108942999582721,3321882686019855,6752708371622431,205903133834692785,418558976041008001,12762672415064932815
%N Numerators of continued fraction convergents to sqrt(240).
%H Vincenzo Librandi, <a href="/A041448/b041448.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 (0,62,0,-1).
%F G.f.: -(x+1)*(x^2-16*x-15) / ((x^2-8*x+1)*(x^2+8*x+1)). - _Vincenzo Librandi_, Nov 02 2013, simplified by _Colin Barker_, Dec 28 2013
%F From _Gerry Martens_, Jul 11 2015: (Start)
%F Interspersion of 2 sequences [a0(n),a1(n)]:
%F a0(n) = ((-15-4*sqrt(15))/(31+8*sqrt(15))^n+(-15+4*sqrt(15))*(31+8*sqrt(15))^n)/2.
%F a1(n) = (1/(31+8*sqrt(15))^n+(31+8*sqrt(15))^n)/2. (End)
%t Numerator[Convergents[Sqrt[240], 30]] (* or *) CoefficientList[Series[(15 + 31 x + 945 x^2 + 1921 x^3 + 945 x^4 - 31 x^5 + 15 x^6 - x^7)/(1 - 3842 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 02 2013 *)
%t a0[n_] := (-15-4*Sqrt[15]+(-15+4*Sqrt[15])*(31+8*Sqrt[15])^(2*n))/(2*(31+8*Sqrt[15])^n) // Simplify
%t a1[n_] := (1+(31+8*Sqrt[15])^(2*n))/(2*(31+8*Sqrt[15])^n) // Simplify
%t Flatten[MapIndexed[{a0[#], a1[#]}&,Range[10]]] (* _Gerry Martens_, Jul 10 2015 *)
%Y Cf. A041449, A040224.
%K nonn,frac,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Colin Barker_, Dec 28 2013
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