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%I #14 May 12 2018 17:44:31
%S 9,19,351,721,13329,27379,506151,1039681,19220409,39480499,729869391,
%T 1499219281,27715816449,56930852179,1052471155671,2161873163521,
%U 39966188099049,82094249361619,1517662676608191
%N Numerators of continued fraction convergents to sqrt(90).
%H Vincenzo Librandi, <a href="/A041160/b041160.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,38,0,-1).
%F G.f.: (1 + x)*(9 + 10*x - x^2) / (1 - 38*x^2 + x^4). [_Bruno Berselli_, Oct 30 2013]
%F a(n) = (2+(-1)^n)*((3-sqrt(10))^(n+1)+(3+sqrt(10))^(n+1))/2. [_Bruno Berselli_, Oct 30 2013]
%t Numerator[Convergents[Sqrt[90], 30]] (* _Vincenzo Librandi_, Oct 29 2013 *)
%t Table[(2 + (-1)^n) ((3 - Sqrt[10])^(n + 1) + (3 + Sqrt[10])^(n + 1))/2, {n, 0, 30}] (* _Bruno Berselli_, Oct 30 2013 *)
%t LinearRecurrence[{0,38,0,-1},{9,19,351,721},30] (* _Harvey P. Dale_, May 12 2018 *)
%Y Cf. A010541, A041161.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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