|
%I #16 Sep 08 2022 08:44:54
%S 11,12,83,95,2173,2268,15781,18049,412859,430908,2998307,3429215,
%T 78441037,81870252,569662549,651532801,14903384171,15554916972,
%U 108232886003,123787802975,2831564551453,2955352354428
%N Numerators of continued fraction convergents to sqrt(141).
%H Vincenzo Librandi, <a href="/A041258/b041258.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,190,0,0,0,-1).
%F G.f.: (11 +12*x +83*x^2 +95x^3 +83x^4 -12x^5 +11x^6 -x^7) / (1 -190*x^4 +x^8). - _Vincenzo Librandi_, Nov 01 2013
%F a(n) = 190*a(n-4)-a(n-8). - _Vincenzo Librandi_, Nov 01 2013
%t Numerator[Convergents[Sqrt[141], 30]] (* or *) CoefficientList[Series[(11 + 12 x + 83 x^2 + 95 x^3 + 83 x^4 - 12 x^5 + 11 x^6 - x^7)/(1 - 190 x^4 + x^8), {x, 0, 25}], x] (* _Vincenzo Librandi_, Oct 31 2013 *)
%o (Magma) I:=[11,12,83,95,2173,2268,15781,18049]; [n le 8 select I[n] else 190*Self(n-4)-Self(n-8): n in [1..25]]; // _Vincenzo Librandi_, Nov 01 2013
%Y Cf. A041259.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
|
