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Numerators of continued fraction convergents to sqrt(545).
2

%I #21 Sep 08 2022 08:44:55

%S 23,47,70,607,677,1961,90883,183727,274610,2380607,2655217,7691041,

%T 356443103,720577247,1077020350,9336740047,10413760397,30164260841,

%U 1397969759083,2826103779007,4224073538090

%N Numerators of continued fraction convergents to sqrt(545).

%H Vincenzo Librandi, <a href="/A042042/b042042.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 3922, 0, 0, 0, 0, 0, -1).

%F G.f.: (23 +47*x +70*x^2 +607*x^3 +677*x^4 +1961*x^5 +677*x^6 -607*x^7 +70*x^8 -47*x^9 +23*x^10 -x^11) / (1 -3922*x^6 +x^12). - _Vincenzo Librandi_, Nov 13 2013

%F a(n) = 3922*a(n-6) - a(n-12). - _Vincenzo Librandi_, Nov 14 2013

%t Numerator[Convergents[Sqrt[545], 30]] (* _Harvey P. Dale_, Oct 28 2012 *)

%t CoefficientList[Series[(23 + 47 x + 70 x^2 + 607 x^3 + 677 x^4 + 1961 x^5 + 677 x^6 - 607 x^7 + 70 x^8 - 47 x^9 + 23 x^10 - x^11)/(1 - 3922 x^6 + x^12), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 13 2013 *)

%o (Magma) I:=[23,47,70,607,677,1961,90883,183727,274610,2380607,2655217, 7691041]; [n le 12 select I[n] else 3922*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Nov 14 2013

%Y Cf. A042043.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.