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Denominators of continued fraction convergents to sqrt(41).
3

%I #23 Sep 08 2022 08:44:53

%S 1,2,5,62,129,320,3969,8258,20485,254078,528641,1311360,16264961,

%T 33841282,83947525,1041211582,2166370689,5373952960,66653806209,

%U 138681565378,344016936965,4266884808958,8877786554881,22022457918720,273147281579521,568317021077762

%N Denominators of continued fraction convergents to sqrt(41).

%H Vincenzo Librandi, <a href="/A041069/b041069.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 (0,0,64,0,0,1).

%F G.f.: -(x^4-2*x^3+5*x^2+2*x+1) / (x^6+64*x^3-1). - _Colin Barker_, Nov 12 2013

%F a(n) = 64*a(n-3) + a(n-6). - _Vincenzo Librandi_, Dec 10 2013

%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[41], n]]], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 21 2011 *)

%t Denominator[Convergents[Sqrt[41], 30]] (* _Vincenzo Librandi_, Dec 10 2013 *)

%t LinearRecurrence[{0,0,64,0,0,1},{1,2,5,62,129,320},40] (* _Harvey P. Dale_, Jun 19 2022 *)

%o (Magma) I:=[1, 2, 5, 62, 129, 320]; [n le 6 select I[n] else 64*Self(n-3)+Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, Dec 10 2013

%Y Cf. A010495, A041068.

%K nonn,cofr,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 12 2013