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A041297 Denominators of continued fraction convergents to sqrt(161). 2

%I #15 Sep 08 2022 08:44:54

%S 1,1,3,13,16,45,61,289,639,928,22911,23839,70589,306195,376784,

%T 1059763,1436547,6805951,15048449,21854400,539554049,561408449,

%U 1662370947,7210892237,8873263184,24957418605,33830681789,160280145761,354390973311,514671119072

%N Denominators of continued fraction convergents to sqrt(161).

%H Vincenzo Librandi, <a href="/A041297/b041297.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 (0,0,0,0,0,0,0,0,0,23550,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^18 -x^17 +3*x^16 -13*x^15 +16*x^14 -45*x^13 +61*x^12 -289*x^11 +639*x^10 -928*x^9 -639*x^8 -289*x^7 -61*x^6 -45*x^5 -16*x^4 -13*x^3 -3*x^2 -x -1) / (x^20 -23550*x^10 +1). - _Colin Barker_, Nov 15 2013

%F a(n) = 23550*a(n-10) - a(n-20). - _Vincenzo Librandi_, Dec 15 2013

%t Denominator[Convergents[Sqrt[161], 30]] (* _Vincenzo Librandi_, Dec 15 2013 *)

%o (Magma) I:=[1,1,3,13,16,45,61,289,639,928,22911,23839, 70589,306195,376784,1059763,1436547,6805951,15048449, 21854400]; [n le 20 select I[n] else 23550*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 15 2013

%Y Cf. A041296, A010210.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 15 2013

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