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%I #16 Sep 08 2022 08:44:55
%S 1,4,17,38,321,6779,54553,115885,518093,2188257,92424887,371887805,
%T 1579976107,3531840019,29834696259,630060461458,5070318387923,
%U 10770697237304,48153107337139,203383126585860,8590244423943259,34564360822358896,146847687713378843
%N Denominators of continued fraction convergents to sqrt(451).
%H Vincenzo Librandi, <a href="/A041859/b041859.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 92942980, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^18 -4*x^17 +17*x^16 -38*x^15 +321*x^14 -6779*x^13 +54553*x^12 -115885*x^11 +518093*x^10 -2188257*x^9 -518093*x^8 -115885*x^7 -54553*x^6 -6779*x^5 -321*x^4 -38*x^3 -17*x^2 -4*x -1)/(x^20 -92942980*x^10 +1). - _Vincenzo Librandi_, Dec 26 2013
%F a(n) = 92942980*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Dec 26 2013
%t Denominator[Convergents[Sqrt[451], 30]] (* or *) CoefficientList[Series[-(x^18 - 4 x^17 + 17 x^16 - 38 x^15 + 321 x^14 - 6779 x^13 + 54553 x^12 - 115885 x^11 + 518093 x^10 - 2188257 x^9 - 518093 x^8 - 115885 x^7 - 54553 x^6 - 6779 x^5 - 321 x^4 - 38 x^3 - 17 x^2 - 4 x - 1)/(x^20 - 92942980 x^10 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 26 2013 *)
%o (Magma) I:=[1,4,17,38,321,6779,54553,115885,518093, 2188257,92424887,371887805,1579976107,3531840019, 29834696259,630060461458,5070318387923,10770697237304, 48153107337139,203383126585860]; [n le 20 select I[n] else 92942980*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 26 2013
%Y Cf. A041858.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Dec 26 2013
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