|
%I #16 Mar 21 2024 06:48:28
%S 0,1,17,256,3825,57121,852992,12737761,190213425,2840463616,
%T 42416740817,633410648641,9458742988800,141247734183361,
%U 2109257269761617,31497611312240896,470354912413851825,7023826074895536481
%N Member r=17 of the family of Chebyshev sequences S_r(n) defined in A092184.
%H Michael De Vlieger, <a href="/A098302/b098302.txt">Table of n, a(n) for n = 0..852</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 (16,-16,1).
%F a(n) = 2*(T(n, 15/2)-1)/13 with twice the Chebyshev polynomials of the first kind evaluated at x=15/2: 2*T(n, 15/2)=A078365(n)= ((15+sqrt(221))^n +(15-sqrt(221))^n)/2^n.
%F a(n) = 15*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.
%F a(n) = 16*a(n-1) - 16*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=17.
%F G.f.: x*(1+x)/((1-x)*(1-15*x+x^2)) = x*(1+x)/(1-16*x+16*x^2-x^3) (from the Stephan link, see A092184).
%t LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 18] &[17] (* _Michael De Vlieger_, Feb 23 2021 *)
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, Oct 18 2004
|
