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 A041073 #31 Jul 09 2025 00:13:49 %S A041073 1,1,2,7,9,52,61,235,296,531,6668,7199,13867,48800,62667,362135, %T A041073 424802,1636541,2061343,3697884,46435951,50133835,96569786,339843193, %U A041073 436412979,2521908088,2958321067,11396871289,14355192356,25752063645,323379956096,349132019741 %N A041073 Denominators of continued fraction convergents to sqrt(43). %H A041073 Vincenzo Librandi, <a href="/A041073/b041073.txt">Table of n, a(n) for n = 0..200</a> %H A041073 Les Tablettes du Chercheur, <a href="https://gallica.bnf.fr/ark:/12148/bpt6k58162334/f11.item">Problem 364</a>, pp. 11, Mai 15 1891. %H A041073 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,6964,0,0,0,0,0,0,0,0,0,-1). %F A041073 G.f.: -(x^18 -x^17 +2*x^16 -7*x^15 +9*x^14 -52*x^13 +61*x^12 -235*x^11 +296*x^10 -531*x^9 -296*x^8 -235*x^7 -61*x^6 -52*x^5 -9*x^4 -7*x^3 -2*x^2 -x -1) / (x^20 -6964*x^10 +1). - _Colin Barker_, Nov 12 2013 %F A041073 a(n) = 6964*a(n-10) - a(n-20). - _Vincenzo Librandi_, Dec 10 2013 %t A041073 Denominator[Convergents[Sqrt[43], 40]] (* _Vincenzo Librandi_, Dec 10 2013 *) %o A041073 (Magma) I:=[1, 1, 2, 7, 9, 52, 61, 235, 296, 531, 6668, 7199, 13867, 48800, 62667, 362135, 424802, 1636541, 2061343, 3697884]; [n le 20 select I[n] else 6964*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 10 2013 %Y A041073 Cf. A010497, A041072. %K A041073 nonn,cofr,frac,easy %O A041073 0,3 %A A041073 _N. J. A. Sloane_ %E A041073 More terms from _Colin Barker_, Nov 12 2013