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%I #18 Sep 08 2022 08:44:54
%S 1,1,2,11,57,68,125,2068,2193,4261,23498,121751,145249,267000,4417249,
%T 4684249,9101498,50191739,260060193,310251932,570312125,9435245932,
%U 10005558057,19440803989,107209578002,555488693999,662698272001,1218186966000,20153689728001
%N Denominators of continued fraction convergents to sqrt(73).
%H Vincenzo Librandi, <a href="/A041129/b041129.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,2136,0,0,0,0,0,0,1).
%F G.f.: -(x^12 -x^11 +2*x^10 -11*x^9 +57*x^8 -68*x^7 +125*x^6 +68*x^5 +57*x^4 +11*x^3 +2*x^2 +x +1) / (x^14 +2136*x^7 -1). - _Colin Barker_, Nov 13 2013
%F a(n) = 2136*a(n-7) + a(n-14). - _Vincenzo Librandi_, Dec 11 2013
%t Denominator/@Convergents[Sqrt[73], 50] (* _Vladimir Joseph Stephan Orlovsky_, Jul 05 2011 *)
%t CoefficientList[Series[-(x^12 - x^11 + 2 x^10 - 11 x^9 + 57 x^8 - 68 x^7 + 125 x^6 + 68 x^5 + 57 x^4 + 11 x^3 + 2 x^2 + x + 1)/(x^14 + 2136 x^7 - 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 11 2013 *)
%o (Magma) I:=[1,1,2,11,57,68,125,2068,2193,4261,23498,121751,145249, 267000]; [n le 14 select I[n] else 2136*Self(n-7)+Self(n-14): n in [1..40]]; // _Vincenzo Librandi_, Dec 11 2013
%Y Cf. A041128, A010151, A020830, A010525.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
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