|
%I #21 Mar 21 2024 06:46:46
%S 0,1,19,324,5491,93025,1575936,26697889,452288179,7662201156,
%T 129805131475,2199025033921,37253620445184,631112522534209,
%U 10691659262636371,181127094942284100,3068468954756193331
%N Member r=19 of the family of Chebyshev sequences S_r(n) defined in A092184.
%H Michael De Vlieger, <a href="/A098304/b098304.txt">Table of n, a(n) for n = 0..814</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 (18,-18,1).
%F a(n) = 2*(T(n, 17/2)-1)/15 with twice the Chebyshev polynomials of the first kind evaluated at x=17/2: 2*T(n, 17/2) = A078367(n) = ((17+sqrt(285))^n + (17-sqrt(285))^n)/2^n.
%F a(n) = 17*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.
%F a(n) = 18*a(n-1) - 18*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=19.
%F G.f.: x*(1+x)/((1-x)*(1-17*x+x^2)) = x*(1+x)/(1-18*x+18*x^2-x^3) (from the Stephan link, see A092184).
%t LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 17] &[19] (* _Michael De Vlieger_, Feb 23 2021 *)
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, Oct 18 2004
|
