A098304 Member r=19 of the family of Chebyshev sequences S_r(n) defined in A092184.
0, 1, 19, 324, 5491, 93025, 1575936, 26697889, 452288179, 7662201156, 129805131475, 2199025033921, 37253620445184, 631112522534209, 10691659262636371, 181127094942284100, 3068468954756193331
Offset: 0
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..814
- 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 (18,-18,1).
Programs
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Mathematica
LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 17] &[19] (* Michael De Vlieger, Feb 23 2021 *)
Formula
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.
a(n) = 17*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.
a(n) = 18*a(n-1) - 18*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=19.
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).