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A041720 Numerators of continued fraction convergents to sqrt(380). 2

%I

%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_, Mov 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,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

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Last modified October 24 01:18 EDT 2021. Contains 348217 sequences. (Running on oeis4.)