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%I A041014 #30 Jun 19 2023 04:24:25
%S A041014 3,10,63,199,1257,3970,25077,79201,500283,1580050,9980583,31521799,
%T A041014 199111377,628855930,3972246957,12545596801,79245827763,250283080090,
%U A041014 1580944308303,4993116004999,31539640338297
%N A041014 Numerators of continued fraction convergents to sqrt(11).
%H A041014 Vincenzo Librandi, <a href="/A041014/b041014.txt">Table of n, a(n) for n = 0..200</a>
%H A041014 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,20,0,-1).
%F A041014 G.f.: (3 + 10*x + 3*x^2 - x^3)/(1 - 20*x^2 + x^4).
%t A041014 Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[11],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 16 2011 *)
%t A041014 Numerator[Convergents[Sqrt[11], 30]] (* _Vincenzo Librandi_, Oct 28 2013 *)
%o A041014 (PARI) A041014=contfracpnqn(c=contfrac(sqrt(11)), #c)[1,][^-1] \\ Discard last element which may be incorrect. Use e.g. \p999 to get more terms, or extend as follows:
%o A041014 {A041014_upto(N,A=Vec(A041014,N))=for(n=#A041014+1,N, A[n]=20*A[n-2]-A[n-4]); A041014=A} \\ _M. F. Hasler_, Nov 01 2019
%Y A041014 Cf. A010468, A041015 (denominators).
%Y A041014 Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041006 (m=6), A041008 (m=7), A041010 (m=8), A005667 (m=10), A041016 (m=12), ..., A042936 (m=1000).
%K A041014 nonn,cofr,frac,easy
%O A041014 0,1
%A A041014 _N. J. A. Sloane_

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