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Denominators of continued fraction convergents to sqrt(459).
2

%I #17 Sep 08 2022 08:44:55

%S 1,2,5,7,33,700,2833,3533,9899,23331,989801,2002933,4995667,6998600,

%T 32990067,699790007,2832150095,3531940102,9896030299,23324000700,

%U 989504059699,2002332120098,4994168299895,6996500419993,32980169979867,699580069997200

%N Denominators of continued fraction convergents to sqrt(459).

%H Vincenzo Librandi, <a href="/A041875/b041875.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 999700, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^18 -2*x^17 +5*x^16 -7*x^15 +33*x^14 -700*x^13 +2833*x^12 -3533*x^11 +9899*x^10 -23331*x^9 -9899*x^8 -3533*x^7 -2833*x^6 -700*x^5 -33*x^4 -7*x^3 -5*x^2 -2*x -1) / (x^20 -999700*x^10 +1). - _Colin Barker_, Nov 26 2013

%F a(n) = 999700*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Dec 26 2013

%t Denominator[Convergents[Sqrt[459], 30]] (* _Vincenzo Librandi_, Dec 26 2013 *)

%o (Magma) I:=[1,2,5,7,33,700,2833,3533,9899,23331,989801, 2002933,4995667,6998600,32990067,699790007,2832150095, 3531940102,9896030299,23324000700]; [n le 20 select I[n] else 999700*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 26 2013

%Y Cf. A041874, A040437.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 26 2013