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%I A041227 #24 Sep 08 2022 08:44:54
%S A041227 1,5,6,11,61,1353,6826,8179,15005,83204,1845493,9310669,11156162,
%T A041227 20466831,113490317,2517253805,12699759342,15217013147,27916772489,
%U A041227 154800875592,3433536035513,17322481053157,20756017088670,38078498141827,211148507797805
%N A041227 Denominators of continued fraction convergents to sqrt(125).
%C A041227 The a(n) terms of this sequence can be constructed with the terms of sequence A049666. For the terms of the periodical sequence of the continued fraction for sqrt(125) see A010186. We observe that its period is five. - _Johannes W. Meijer_, Jun 12 2010
%H A041227 Vincenzo Librandi, <a href="/A041227/b041227.txt">Table of n, a(n) for n = 0..200</a>
%H A041227 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1364,0,0,0,0,1).
%F A041227 a(5*n) = A049666(3*n+1), a(5*n+1) = (A049666(3*n+2) - A049666(3*n+1))/2, a(5*n+2) = (A049666(3*n+2)+A049666(3*n+1))/2, a(5*n+3):= A049666(3*n+2) and a(5*n+4) = A049666(3*n+3)/2. - _Johannes W. Meijer_, Jun 12 2010
%F A041227 G.f.: -(x^8 -5*x^7 +6*x^6 -11*x^5 +61*x^4 +11*x^3 +6*x^2 +5*x +1) / ((x^2 +4*x -1)*(x^4 -7*x^3 +19*x^2 -3*x +1)*(x^4 +3*x^3 +19*x^2 +7*x +1)). - _Colin Barker_, Nov 12 2013
%F A041227 a(n) = 1364*a(n-5) + a(n-10). - _Vincenzo Librandi_, Dec 13 2013
%t A041227 Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[125], n]]], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 23 2011 *)
%t A041227 Denominator[Convergents[Sqrt[125], 30]]  (* _Vincenzo Librandi_, Dec 13 2013 *)
%t A041227 LinearRecurrence[{0,0,0,0,1364,0,0,0,0,1},{1,5,6,11,61,1353,6826,8179,15005,83204},30] (* _Harvey P. Dale_, Apr 29 2022 *)
%o A041227 (Magma) I:=[1, 5, 6, 11, 61, 1353, 6826, 8179, 15005, 83204]; [n le 10 select I[n] else 1364*Self(n-5)+Self(n-10): n in [1..40]]; // _Vincenzo Librandi_, Dec 13 2013
%Y A041227 Cf. A041226, A010186, A041019, A041047, A041091, A041151, A041227, A041319, A041427, A041551.
%K A041227 nonn,frac,easy
%O A041227 0,2
%A A041227 _N. J. A. Sloane_.

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