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%I A042626 #17 Sep 08 2022 08:44:55
%S A042626 29,842,48865,1417927,82288631,2387788226,138574005739,4021033954657,
%T A042626 233358543375845,6771418791854162,392975648470917241,
%U A042626 11403065224448454151,661770758666481257999,19202755066552404936122
%N A042626 Numerators of continued fraction convergents to sqrt(843).
%H A042626 Vincenzo Librandi, <a href="/A042626/b042626.txt">Table of n, a(n) for n = 0..200</a>
%H A042626 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1684, 0, -1).
%F A042626 G.f.: (29 +842*x +29*x^2 -x^3)/(1 -1684*x^2 +x^4). - _Vincenzo Librandi_, Nov 30 2013
%F A042626 a(n) = 1684*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 30 2013
%t A042626 Numerator[Convergents[Sqrt[843], 30]] (* or *) CoefficientList[Series[(29 + 842 x + 29 x^2 - x^3)/(1 - 1684 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 30 2013 *)
%o A042626 (Magma) I:=[29,842,48865,1417927]; [n le 4 select I[n] else 1684*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 30 2013
%Y A042626 Cf. A042627.
%K A042626 nonn,cofr,frac,easy
%O A042626 0,1
%A A042626 _N. J. A. Sloane_.

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