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%I #12 Feb 24 2021 04:14:58
%S 0,1,18,289,4608,73441,1170450,18653761,297289728,4737981889,
%T 75510420498,1203428746081,19179349516800,305666163522721,
%U 4871479266846738,77638002106025089,1237336554429554688
%N Member r=18 of the family of Chebyshev sequences S_r(n) defined in A092184.
%H Michael De Vlieger, <a href="/A098303/b098303.txt">Table of n, a(n) for n = 0..832</a>
%H 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 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-17,1).
%F a(n) = (T(n, 8)-1)/7 with Chebyshev's polynomials of the first kind evaluated at x=8: T(n, 8)=A001081(n)= ((8+3*sqrt(7))^n + (8-3*sqrt(7))^n)/2.
%F a(n) = 16*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.
%F a(n) = 17*a(n-1) - 17*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=18.
%F G.f.: x*(1+x)/((1-x)*(1-16*x+x^2)) = x*(1+x)/(1-17*x+17*x^2-x^3) (from the Stephan link, see A092184).
%t LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 17] &[18] (* _Michael De Vlieger_, Feb 23 2021 *)
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, Oct 18 2004
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