|
%I #30 Jun 19 2023 04:24:25
%S 3,10,63,199,1257,3970,25077,79201,500283,1580050,9980583,31521799,
%T 199111377,628855930,3972246957,12545596801,79245827763,250283080090,
%U 1580944308303,4993116004999,31539640338297
%N Numerators of continued fraction convergents to sqrt(11).
%H Vincenzo Librandi, <a href="/A041014/b041014.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 (0,20,0,-1).
%F G.f.: (3 + 10*x + 3*x^2 - x^3)/(1 - 20*x^2 + x^4).
%t Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[11],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 16 2011 *)
%t Numerator[Convergents[Sqrt[11], 30]] (* _Vincenzo Librandi_, Oct 28 2013 *)
%o (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_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 Cf. A010468, A041015 (denominators).
%Y 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 nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_
|
