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A041897 Denominators of continued fraction convergents to sqrt(470). 2

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

%S 1,1,3,25,53,78,3329,3407,10143,84551,179245,263796,11258677,11522473,

%T 34303623,285951457,606206537,892157994,38076842285,38969000279,

%U 116014842843,967087743023,2050190328889,3017278071912,128775869349193,131793147421105

%N Denominators of continued fraction convergents to sqrt(470).

%H Vincenzo Librandi, <a href="/A041897/b041897.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 3382, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^10 -x^9 +3*x^8 -25*x^7 +53*x^6 -78*x^5 -53*x^4 -25*x^3 -3*x^2 -x -1) / (x^12 -3382*x^6 +1). - _Colin Barker_, Nov 27 2013

%F a(n) = 3382*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 26 2013

%t Denominator[Convergents[Sqrt[470], 30]] (* _Vincenzo Librandi_, Dec 26 2013 *)

%o (Magma) I:=[1,1,3,25,53,78,3329,3407,10143,84551,179245, 263796]; [n le 12 select I[n] else 3382*Self(n-6)-Self(n-12): n in [1..50]]; // _Vincenzo Librandi_, Dec 26 2013

%Y Cf. A041896, A040448.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 27 2013

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)