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

0,3

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).

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).

Mathematica

LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 17] &[18] (* Michael De Vlieger, Feb 23 2021 *)

Crossrefs

Sequence in context: A294327 A286725 A226998 * A232154 A014899 A048447

Adjacent sequences: A098300 A098301 A098302 * A098304 A098305 A098306

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 18 2004

Status

approved