A098303 Member r=18 of the family of Chebyshev sequences S_r(n) defined in A092184.
0, 1, 18, 289, 4608, 73441, 1170450, 18653761, 297289728, 4737981889, 75510420498, 1203428746081, 19179349516800, 305666163522721, 4871479266846738, 77638002106025089, 1237336554429554688
Offset: 0
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..832
- S. Barbero, U. Cerruti, and N. Murru, On polynomial solutions of the Diophantine equation (x + y - 1)^2 = wxy, Rendiconti Sem. Mat. Univ. Pol. Torino (2020) Vol. 78, No. 1, 5-12.
- Index entries for sequences related to Chebyshev polynomials.
- Index entries for linear recurrences with constant coefficients, signature (17,-17,1).
Programs
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Mathematica
LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 17] &[18] (* Michael De Vlieger, Feb 23 2021 *)
Formula
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.
a(n) = 16*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.
a(n) = 17*a(n-1) - 17*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=18.
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).