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 A041612 #36 Oct 30 2024 18:37:26 %S A041612 18,649,23382,842401,30349818,1093435849,39394040382,1419278889601, %T A041612 51133434066018,1842222905266249,66371158023650982, %U A041612 2391203911756701601,86149711981264908618,3103780835237293411849,111822259780523827735182,4028705132934095091878401 %N A041612 Numerators of continued fraction convergents to sqrt(325). %C A041612 a(2*n) and b(2*n) = A041613(2*n) give all (positive integer) solutions to the Pell equation a^2 - 13*b^2 = -1. a(2*n+1) and b(2*n+1) = A041613(2*n+1) give all (positive integer) solutions to the Pell equation a^2 - 13*b^2 = 1. - _Robert FERREOL_, Oct 09 2024 %H A041612 Vincenzo Librandi, <a href="/A041612/b041612.txt">Table of n, a(n) for n = 0..200</a> %H A041612 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a> %H A041612 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (36,1). %F A041612 From _Philippe Deléham_, Nov 23 2008: (Start) %F A041612 a(n) = 36*a(n-1) + a(n-2), n > 1; a(0)=18, a(1)=649. %F A041612 G.f.: (18+x)/(1-36*x-x^2). (End) %F A041612 a(n) = ((18 + 5*sqrt(13))^(n+1) + (18 - 5*sqrt(13))^(n+1))/2. - _Robert FERREOL_, Oct 09 2024 %t A041612 Numerator[Convergents[Sqrt[325], 30]] (* _Vincenzo Librandi_, Nov 04 2013 *) %Y A041612 Cf. A040306 (continued fraction), A041613 (denominators), A295330. %K A041612 nonn,cofr,frac,easy %O A041612 0,1 %A A041612 _N. J. A. Sloane_ %E A041612 Additional term from _Colin Barker_, Nov 09 2013