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%I #14 Jul 17 2023 18:49:18
%S 1,1,3,4,15,19,129,1051,6435,7486,28893,36379,101651,138030,5622851,
%T 5760881,17144613,22905494,85861095,108766589,738460629,6016451621,
%U 36837170355,42853621976,165398036283,208251658259,581901352801,790153011060,32188021795201,32978174806261
%N Denominators of continued fraction convergents to sqrt(430).
%H Vincenzo Librandi, <a href="/A041819/b041819.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5724502, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^26 -x^25 +3*x^24 -4*x^23 +15*x^22 -19*x^21 +129*x^20 -1051*x^19 +6435*x^18 -7486*x^17 +28893*x^16 -36379*x^15 +101651*x^14 -138030*x^13 -101651*x^12 -36379*x^11 -28893*x^10 -7486*x^9 -6435*x^8 -1051*x^7 -129*x^6 -19*x^5 -15*x^4 -4*x^3 -3*x^2 -x -1)/(x^28 -5724502*x^14 +1). - _Vincenzo Librandi_, Dec 25 2013
%F a(n) = 5724502*a(n-14) - a(n-28) for n>27. - _Vincenzo Librandi_, Dec 25 2013
%t Denominator[Convergents[Sqrt[430], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 3 x^24 - 4 x^23 + 15 x^22 - 19 x^21 + 129 x^20 - 1051 x^19 + 6435 x^18 - 7486 x^17 + 28893 x^16 - 36379 x^15 + 101651 x^14 - 138030 x^13 - 101651 x^12 - 36379 x^11 - 28893 x^10 - 7486 x^9 - 6435 x^8 - 1051 x^7 - 129 x^6 - 19 x^5 - 15 x^4 - 4 x^3 -3 x^2 - x - 1)/(x^28 - 5724502 x^14 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 25 2013 *)
%Y Cf. A041818.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Dec 25 2013
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