A041379 - OEIS

%I #18 Sep 08 2022 08:44:54

%S 1,3,4,7,46,53,99,350,9899,30047,39946,69993,459904,529897,989801,

%T 3499300,98970201,300409903,399380104,699790007,4598120146,5297910153,

%U 9896030299,34986001050,989504059699,3003498180147,3993002239846,6996500419993,45972004759804

%N Denominators of continued fraction convergents to sqrt(204).

%H Vincenzo Librandi, <a href="/A041379/b041379.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 (0,0,0,0,0,0,0,9998,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^14 -3*x^13 +4*x^12 -7*x^11 +46*x^10 -53*x^9 +99*x^8 -350*x^7 -99*x^6 -53*x^5 -46*x^4 -7*x^3 -4*x^2 -3*x -1) / ((x^8 -100*x^4 +1)*(x^8 +100*x^4 +1)). - _Colin Barker_, Nov 16 2013

%F a(n) = 9998*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 16 2013

%t Denominator[Convergents[Sqrt[204], 30]] (* _Vincenzo Librandi_, Dec 16 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,9998,0,0,0,0,0,0,0,-1},{1,3,4,7,46,53,99,350,9899,30047,39946,69993,459904,529897,989801,3499300},30] (* _Harvey P. Dale_, Jul 22 2021 *)

%o (Magma) I:=[1,3,4,7,46,53,99,350,9899,30047,39946,69993, 459904,529897,989801,3499300]; [n le 16 select I[n] else 9998*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 16 2013

%Y Cf. A041378, A040189.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 16 2013