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 A075835 #35 Jul 15 2025 10:52:18
%S A075835 0,3,33,360,3927,42837,467280,5097243,55602393,606529080,6616217487,
%T A075835 72171863277,787274278560,8587845200883,93679022931153,
%U A075835 1021881407041800,11147016454528647,121595299592773317
%N A075835 Numbers k such that 13*k^2 + 4 is a square.
%C A075835 Lim_{n->infinity} a(n)/a(n-1) = (11 + sqrt(13))/2.
%D A075835 A. H. Beiler, "The Pellian", ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover, New York, New York, pp. 248-268, 1966.
%D A075835 L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, pp. 341-400.
%D A075835 Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics Source Series, V. 16); American Mathematical Society, Providence, Rhode Island, 1999, pp. 139-147.
%D A075835 S. Falcon, Relationships between Some k-Fibonacci Sequences, Applied Mathematics, 2014, 5, 2226-2234; http://www.scirp.org/journal/am; http://dx.doi.org/10.4236/am.2014.515216
%H A075835 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A075835 J. J. O'Connor and E. F. Robertson, <a href="https://mathshistory.st-andrews.ac.uk/HistTopics/Pell/">Pell's Equation</a>
%H A075835 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PellEquation.html">Pell Equation</a>
%H A075835 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-1).
%F A075835 a(n) = ((11 + 3*sqrt(13))^n - (11 - 3*sqrt(13))^n) / ((2^n) * sqrt(13)).
%F A075835 From _Philippe Deléham_, Nov 17 2008: (Start)
%F A075835 a(n) = 11*a(n-1) - a(n-2) with a(1)=0 and a(2)=3.
%F A075835 G.f.: 3x^2/(1-11x+x^2). (End)
%F A075835 a(n) = A006190(2*n). - _Vladimir Reshetnikov_, Sep 16 2016
%t A075835 LinearRecurrence[{11,-1},{0,3},20] (* _Harvey P. Dale_, Dec 27 2011 *)
%t A075835 Table[Fibonacci[2n, 3], {n, 0, 20}] (* _Vladimir Reshetnikov_, Sep 16 2016 *)
%Y A075835 Cf. A006190.
%K A075835 nonn,easy
%O A075835 1,2
%A A075835 _Gregory V. Richardson_, Oct 14 2002