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 A202299 #25 Dec 16 2024 18:12:33
%S A202299 0,4,136,4620,156944,5331476,181113240,6152518684,209004522016,
%T A202299 7100001229860,241191037293224,8193395266739756,278334248031858480,
%U A202299 9455171037816448564,321197481037727392696,10911259184244914903100
%N A202299 y-values in the solution to x^2 - 18*y^2 = 1.
%C A202299 The corresponding values of x of this Pell equation are in A056771.
%H A202299 Vincenzo Librandi, <a href="/A202299/b202299.txt">Table of n, a(n) for n = 1..200</a>
%H A202299 Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
%H A202299 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (34,-1).
%F A202299 a(n) = 34*a(n-1)-a(n-2) with a(1)=0, a(2)=4.
%F A202299 G.f.: 4*x^2/(1-34*x+x^2).
%F A202299 a(n) = (1/3)*A001542(2n-2). - _Bruno Berselli_, Dec 19 2011
%t A202299 LinearRecurrence[{34,-1},{0,4},30]
%t A202299 With[{c=6*Sqrt[2]},Table[((17-2c)^n-(17+2c)^n)/-c,{n,0,20}]]//Simplify (* _Harvey P. Dale_, Dec 16 2024 *)
%o A202299 (Magma) I:=[0, 4]; [n le 2 select I[n] else 34*Self(n-1)-Self(n-2): n in [1..20]];
%o A202299 (Maxima) makelist(expand(((3+2*sqrt(2))^(2*n-2)-(3-2*sqrt(2))^(2*n-2))/(6*sqrt(2))), n, 1, 16); /* _Bruno Berselli, Dec 19 2011 */
%Y A202299 Cf. A001542, A056771.
%K A202299 nonn,easy
%O A202299 1,2
%A A202299 _Vincenzo Librandi_, Dec 18 2011