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A041105 Denominators of continued fraction convergents to sqrt(60).

%I A041105 #26 Sep 08 2022 08:44:53
%S A041105 1,1,3,4,59,63,185,248,3657,3905,11467,15372,226675,242047,710769,
%T A041105 952816,14050193,15003009,44056211,59059220,870885291,929944511,
%U A041105 2730774313,3660718824,53980837849,57641556673,169263951195,226905507868,3345941061347,3572846569215
%N A041105 Denominators of continued fraction convergents to sqrt(60).
%C A041105 Interspersion of 4 linear recurrences with constant coefficients. - _Gerry Martens_, Jun 10 2015
%H A041105 Vincenzo Librandi, <a href="/A041105/b041105.txt">Table of n, a(n) for n = 0..200</a>
%H A041105 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,62,0,0,0,-1).
%F A041105 G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / ((x^4-8*x^2+1)*(x^4+8*x^2+1)). - _Colin Barker_, Nov 12 2013
%F A041105 a(n) = 62*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 11 2013
%p A041105 numtheory:-cfrac(sqrt(60),100,'con','den'):
%p A041105 den[1..-2]; # _Robert Israel_, Jun 09 2015
%t A041105 Denominator[Convergents[Sqrt[60], 30]] (* _Vincenzo Librandi_, Dec 11 2013 *)
%t A041105 d0 := LinearRecurrence[{62, -1}, {1, 59}, 20]
%t A041105 d1 := LinearRecurrence[{62, -1}, {1, 63}, 20] (* A258684  *)
%t A041105 d2 := LinearRecurrence[{62, -1}, {3, 185}, 20]
%t A041105 d3 := LinearRecurrence[{62, -1}, {4, 248}, 20]
%t A041105 Flatten[MapIndexed[{d0[[#]] , d1[[#]], d2[[#]] , d3[[#]]} &,
%t A041105   Range[10]]] (* _Gerry Martens_, Jun 09 2015 *)
%t A041105 LinearRecurrence[{0, 0, 0, 62, 0, 0, 0, -1},{1, 1, 3, 4, 59, 63, 185, 248},30] (* _Ray Chandler_, Aug 03 2015 *)
%o A041105 (Magma) I:=[1, 1, 3, 4, 59, 63, 185, 248]; [n le 8 select I[n] else 62*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 11 2013
%Y A041105 Cf. A041104, A040052, A020817, A010513.
%Y A041105 Cf. A258684.
%K A041105 nonn,cofr,easy,frac
%O A041105 0,3
%A A041105 _N. J. A. Sloane_
%E A041105 More terms from _Colin Barker_, Nov 12 2013