This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A041151 #28 Jul 09 2025 00:20:42
%S A041151 1,4,5,9,41,747,3029,3776,6805,30996,564733,2289928,2854661,5144589,
%T A041151 23433017,426938895,1731188597,2158127492,3889316089,17715391848,
%U A041151 322766369353,1308780869260,1631547238613,2940328107873,13392859670105,244011802169763,989440068349157
%N A041151 Denominators of continued fraction convergents to sqrt(85).
%C A041151 From _Johannes W. Meijer_, Jun 12 2010: (Start)
%C A041151 The a(n) terms of this sequence can be constructed with the terms of sequence A099371.
%C A041151 For the terms of the periodic sequence of the continued fraction for sqrt(85) see A010158. We observe that its period is five. The decimal expansion of sqrt(85) is A010536. (End)
%H A041151 Vincenzo Librandi, <a href="/A041151/b041151.txt">Table of n, a(n) for n = 0..200</a>
%H A041151 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,756,0,0,0,0,1).
%F A041151 From _Johannes W. Meijer_, Jun 12 2010: (Start)
%F A041151 a(5*n) = A099371(3*n+1), a(5*n+1) = (A099371(3*n+2)-A099371(3*n+1))/2, a(5*n+2) = (A099371(3*n+2)+A099371(3*n+1))/2, a(5*n+3):= A099371(3*n+2) and a(5*n+4) = A099371(3*n+3)/2. (End)
%F A041151 G.f.: -(x^8-4*x^7+5*x^6-9*x^5+41*x^4+9*x^3+5*x^2+4*x+1) / (x^10+756*x^5-1). - _Colin Barker_, Nov 11 2013
%F A041151 a(n) = 756*a(n-5) + a(n-10). - _Vincenzo Librandi_, Dec 12 2013
%t A041151 Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[85], n]]], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 23 2011 *)
%t A041151 Denominator[Convergents[Sqrt[85], 30]] (* _Vincenzo Librandi_, Dec 12 2013 *)
%o A041151 (Magma) I:=[1, 4, 5, 9, 41, 747, 3029, 3776, 6805, 30996]; [n le 10 select I[n] else 756*Self(n-5)+Self(n-10): n in [1..30]]; // _Vincenzo Librandi_, Dec 12 2013
%Y A041151 Cf. A041150, A041019, A041047, A041091, A041151, A041227, A041319, A041427, A041551.
%K A041151 nonn,frac,easy
%O A041151 0,2
%A A041151 _N. J. A. Sloane_