%I #21 Nov 11 2023 03:35:53
%S 19,39,1501,3041,117059,237159,9129101,18495361,711952819,1442400999,
%T 55523190781,112488782561,4330096928099,8772682638759,337692037200941,
%U 684156757040641,26335648804745299,53355454366531239
%N Numerators of continued fraction convergents to sqrt(380).
%H Vincenzo Librandi, <a href="/A041720/b041720.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 (0,78,0,-1).
%F G.f.: (19+39*x+19*x^2-x^3)/(1-78*x^2+x^4). - _Vincenzo Librandi_, Nov 07 2013
%F a(n) = 78*a(n-2)-a(n-4). - _Vincenzo Librandi_, Nov 07 2013
%t Numerator[Convergents[Sqrt[380], 30]] (* or *) CoefficientList[Series[(19 + 39 x + 19 x^2 - x^3)/(1 - 78 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 07 2013 *)
%o (Magma) I:=[19,39,1501,3041]; [n le 4 select I[n] else 78*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 07 2013
%Y Cf. A041721.
%K nonn,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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