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 A218735 #57 Nov 30 2024 17:37:55
%S A218735 5,6,9,13,22,33,57,86,149,225,390,589,1021,1542,2673,4037,6998,10569,
%T A218735 18321,27670,47965,72441,125574,189653,328757,496518,860697,1299901,
%U A218735 2253334,3403185,5899305,8909654,15444581,23325777,40434438,61067677,105858733
%N A218735 Values of x in the solutions to x^2 - 3xy + y^2 + 29 = 0, where 0 < x < y.
%C A218735 The corresponding values of y are given by a(n+2).
%C A218735 Positive values of x (or y) satisfying x^2 - 18xy + y^2 + 1856 = 0.
%H A218735 Colin Barker, <a href="/A218735/b218735.txt">Table of n, a(n) for n = 1..1000</a>
%H A218735 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-1).
%F A218735 a(n) = 3*a(n-2)-a(n-4).
%F A218735 G.f.: -x*(x-1)*(5*x^2+11*x+5) / ((x^2-x-1)*(x^2+x-1)).
%e A218735 13 is in the sequence because (x, y) = (13, 33) is a solution to x^2 - 3xy + y^2 + 29 = 0.
%t A218735 LinearRecurrence[{0,3,0,-1},{5,6,9,13},40] (* _Harvey P. Dale_, Nov 30 2024 *)
%o A218735 (PARI) Vec(-x*(x-1)*(5*x^2+11*x+5)/((x^2-x-1)*(x^2+x-1)) + O(x^100))
%Y A218735 Cf. A001519, A005248, A055819, A237132, A237133.
%K A218735 nonn,easy
%O A218735 1,1
%A A218735 _Colin Barker_, Feb 05 2014