|
%I #21 Sep 08 2022 08:44:54
%S 12,73,1764,10657,257532,1555849,37597908,227143297,5489037036,
%T 33161365513,801361809348,4841332221601,116993335127772,
%U 706801342988233,17080225566845364,103188154744060417,2493595939424295372
%N Numerators of continued fraction convergents to sqrt(148).
%H Vincenzo Librandi, <a href="/A041270/b041270.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,146,0,-1).
%F G.f.: (12+73*x+12*x^2-x^3)/(1-146*x^2+x^4). - _Vincenzo Librandi_, Nov 01 2013
%F a(n) = 146*a(n-2)-a(n-4). - _Vincenzo Librandi_, Nov 01 2013
%t Numerator[Convergents[Sqrt[148], 30]] (* or *) CoefficientList[Series[(12 + 73 x + 12 x^2 - x^3)/(1 - 146 x^2 + x^4), {x, 0, 25}], x](* _Vincenzo Librandi_, Nov 01 2013 *)
%t LinearRecurrence[{0,146,0,-1},{12,73,1764,10657},20] (* _Harvey P. Dale_, Apr 28 2018 *)
%o (Magma) I:=[12,73,1764,10657]; [n le 4 select I[n] else 146*Self(n-2)-Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Nov 01 2013
%Y Cf. A041271.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
|
