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 A098300 #16 Mar 21 2024 06:47:25
%S A098300 0,1,15,196,2535,32761,423360,5470921,70698615,913611076,11806245375,
%T A098300 152567578801,1971572279040,25477872048721,329240764354335,
%U A098300 4254652064557636,54981236074894935,710501416909076521
%N A098300 Member r=15 of the family of Chebyshev sequences S_r(n) defined in A092184.
%H A098300 Michael De Vlieger, <a href="/A098300/b098300.txt">Table of n, a(n) for n = 0..900</a>
%H A098300 S. Barbero, U. Cerruti, and N. Murru, <a href="http://www.seminariomatematico.polito.it/rendiconti/78-1/BarberoCerrutiMurru.pdf">On polynomial solutions of the Diophantine equation (x + y - 1)^2 = wxy</a>, Rendiconti Sem. Mat. Univ. Pol. Torino (2020) Vol. 78, No. 1, 5-12.
%H A098300 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A098300 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-14,1).
%F A098300 a(n) = 2*(T(n, 13/2)-1)/11 with twice the Chebyshev polynomials of the first kind evaluated at x=13/2: 2*T(n, 13/2)=A078363(n)=((13+sqrt(165))^n + (13-sqrt(165))^n)/2^n.
%F A098300 a(n) = 13*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.
%F A098300 a(n) = 14*a(n-1) - 14*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=15.
%F A098300 G.f.: x*(1+x)/((1-x)*(1-13*x+x^2)) = x*(1+x)/(1-14*x+14*x^2-x^3) (from the Stephan link, see A092184).
%t A098300 LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 18] &[15] (* _Michael De Vlieger_, Feb 23 2021 *)
%K A098300 nonn,easy
%O A098300 0,3
%A A098300 _Wolfdieter Lang_, Oct 18 2004