A098300 Member r=15 of the family of Chebyshev sequences S_r(n) defined in A092184.
0, 1, 15, 196, 2535, 32761, 423360, 5470921, 70698615, 913611076, 11806245375, 152567578801, 1971572279040, 25477872048721, 329240764354335, 4254652064557636, 54981236074894935, 710501416909076521
Offset: 0
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..900
- 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 (14,-14,1).
Programs
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Mathematica
LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 18] &[15] (* Michael De Vlieger, Feb 23 2021 *)
Formula
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.
a(n) = 13*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.
a(n) = 14*a(n-1) - 14*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=15.
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).