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 A041319 #28 Jul 09 2025 00:37:33
%S A041319 1,6,7,13,85,2223,13423,15646,29069,190060,4970629,30013834,34984463,
%T A041319 64998297,424974245,11114328667,67110946247,78225274914,145336221161,
%U A041319 950242601880,24851643870041,150060105822126,174911749692167,324971855514293,2124742882777925
%N A041319 Denominators of continued fraction convergents to sqrt(173).
%C A041319 The a(n) terms of this sequence can be constructed with the terms of sequence A140455. For the terms of the periodical sequence of the continued fraction for sqrt(173) see A010217. We observe that its period is five. - _Johannes W. Meijer_, Jun 12 2010
%H A041319 Vincenzo Librandi, <a href="/A041319/b041319.txt">Table of n, a(n) for n = 0..200</a>
%H A041319 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 2236, 0, 0, 0, 0, 1).
%F A041319 a(5*n) = A140455(3*n+1), a(5*n+1) = (A140455(3*n+2) - A140455(3*n+1))/2, a(5*n+2) = (A140455(3*n+2)+A140455(3*n+1))/2, a(5*n+3) = A140455(3*n+2) and a(5*n+4) = A140455(3*n+3)/2. - _Johannes W. Meijer_, Jun 12 2010
%F A041319 G.f.: -(x^8-6*x^7+7*x^6-13*x^5+85*x^4+13*x^3+7*x^2+6*x+1) / (x^10+2236*x^5-1). - _Colin Barker_, Nov 12 2013
%F A041319 a(n) = 2236*a(n-5) + a(n-10). - _Vincenzo Librandi_, Dec 15 2013
%t A041319 Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[173], n]]], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 23 2011 *)
%t A041319 Denominator[Convergents[Sqrt[173], 30]] (* _Vincenzo Librandi_, Dec 15 2013 *)
%t A041319 LinearRecurrence[{0,0,0,0,2236,0,0,0,0,1},{1,6,7,13,85,2223,13423,15646,29069,190060},30] (* _Harvey P. Dale_, Sep 19 2020 *)
%o A041319 (Magma) I:=[1,6,7,13,85,2223,13423,15646,29069,190060]; [n le 10 select I[n] else 2236*Self(n-5)+Self(n-10): n in [1..40]]; // _Vincenzo Librandi_, Dec 15 2013
%Y A041319 Cf. A041318, A010217, A041019, A041047, A041091, A041151, A041227, A041319, A041427 and A041551.
%K A041319 nonn,easy,frac
%O A041319 0,2
%A A041319 _N. J. A. Sloane_