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%I #13 Sep 08 2022 08:44:55
%S 1,1,4,9,13,22,35,232,267,499,766,2031,6859,8890,380239,389129,
%T 1547626,3484381,5032007,8516388,13548395,89806758,103355153,
%U 193161911,296517064,786196039,2655105181,3441301220,147189756421,150631057641,599082929344
%N Denominators of continued fraction convergents to sqrt(474).
%H Vincenzo Librandi, <a href="/A041905/b041905.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, 387098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^26 -x^25 +4*x^24 -9*x^23 +13*x^22 -22*x^21 +35*x^20 -232*x^19 +267*x^18 -499*x^17 +766*x^16 -2031*x^15 +6859*x^14 -8890*x^13 -6859*x^12 -2031*x^11 -766*x^10 -499*x^9 -267*x^8 -232*x^7 -35*x^6 -22*x^5 -13*x^4 -9*x^3 -4*x^2 -x -1)/(x^28 -387098*x^14 +1). - _Vincenzo Librandi_, Dec 26 2013
%F a(n) = 387098*a(n-14) - a(n-28) for n>27. - _Vincenzo Librandi_, Dec 26 2013
%t Denominator[Convergents[Sqrt[474], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 4 * x^24 - 9 * x^23 + 13 * x^22 - 22 * x^21 + 35 * x^20 - 232 * x^19 + 267 * x^18 - 499 * x^17 + 766 * x^16 - 2031 * x^15 + 6859 * x^14 - 8890 * x^13 - 6859 * x^12 - 2031 * x^11 - 766 * x^10 - 499 * x^9 - 267 * x^8 - 232 * x^7 - 35 * x^6 - 22 * x^5 - 13 * x^4 - 9 * x^3 - 4 * x^2 - x - 1)/(x^28 - 387098 * x^14 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 26 2013 *)
%o (Magma) I:=[1,1,4,9,13,22,35,232,267,499,766,2031,6859, 8890,380239,389129,1547626,3484381,5032007,8516388, 13548395,89806758,103355153,193161911,296517064, 786196039,2655105181,3441301220]; [n le 28 select I[n] else 387098*Self(n-14)-Self(n-28): n in [1..50]]; // _Vincenzo Librandi_, Dec 26 2013
%Y Cf. A041904.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Dec 26 2013
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