Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #24 Oct 20 2024 18:04:09
%S 30,91,5490,16561,999150,3014011,181839810,548533441,33093846270,
%T 99830072251,6022898181330,18168524616241,1096134375155790,
%U 3306571650083611,199490433380172450,601777871790600961,36306162740816230110,109520266094239291291,6607522128395173707570
%N Numerators of continued fraction convergents to sqrt(920).
%H Vincenzo Librandi, <a href="/A042778/b042778.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 (0,182,0,-1).
%F G.f.: (30 + 91*x + 30*x^2 - x^3)/(1 - 182*x^2 + x^4). - _Vincenzo Librandi_, Dec 04 2013, simplified by _Colin Barker_, Dec 23 2013
%F a(n) = 33122*a(n-4) - a(n-8) = 182*a(n-2) - a(n-4). - _Vincenzo Librandi_, Dec 04 2013, reduced by _Bruno Berselli_, Dec 23 2013
%t Numerator[Convergents[Sqrt[920], 30]] (* or *) CoefficientList[Series[(30 + 91 x + 30 x^2 - x^3)/(1 - 182 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 04 2013 *)
%t LinearRecurrence[{0,182,0,-1},{30,91,5490,16561},30] (* _Harvey P. Dale_, Oct 20 2024 *)
%o (Magma) I:=[30, 91, 5490, 16561]; [n le 4 select I[n] else 182*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 04 2013, reduced by _Bruno Berselli_, Dec 23 2013
%Y Cf. A042779, A040889.
%K nonn,frac,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Vincenzo Librandi_, Dec 04 2013