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A041228 Numerators of continued fraction convergents to sqrt(126). 2

%I

%S 11,45,101,449,9979,40365,90709,403201,8961131,36247725,81456581,

%T 362074049,8047085659,32550416685,73147919029,325142092801,

%U 7226273960651,29230237935405,65686749831461,291977237261249,6489185969578939,26248721115577005

%N Numerators of continued fraction convergents to sqrt(126).

%H Vincenzo Librandi, <a href="/A041228/b041228.txt">Table of n, a(n) for n = 0..150</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,898,0,0,0,-1).

%F G.f.: (11 +45*x +101*x^2 +449*x^3 +101*x^4 -45*x^5 +11*x^6 -x^7) / ((1 -30*x^2 +x^4)*(1 +30*x^2 +x^4)). [_Bruno Berselli_, Oct 31 2013]

%t Numerator[Convergents[Sqrt[126], 30]] (* _Vincenzo Librandi_, Oct 31 2013 *)

%t LinearRecurrence[{0, 0, 0, 898, 0, 0, 0, -1}, {11, 45, 101, 449, 9979, 40365, 90709, 403201}, 30] (* _Bruno Berselli_, Oct 31 2013 *)

%o (MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((11+45*x+101*x^2+449*x^3+101*x^4-45*x^5+11*x^6-x^7)/((1-30*x^2+x^4)*(1+30*x^2+x^4)))); // _Bruno Berselli_, Oct 31 2013

%Y Cf. A041229.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

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Last modified January 28 09:52 EST 2020. Contains 331319 sequences. (Running on oeis4.)