A098308 Unsigned member r=-8 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 8, 81, 800, 7921, 78408, 776161, 7683200, 76055841, 752875208, 7452696241, 73774087200, 730288175761, 7229107670408, 71560788528321, 708378777612800, 7012226987599681, 69413891098384008, 687126683996240401

Offset: 0

Author

Wolfdieter Lang, Oct 18 2004

Keywords

• nonn
• easy

Comments

((-1)^(n+1))*a(n) = S_{-8}(n), n>=0, defined in A092184.

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (9,9,-1).

Programs

Mathematica

LinearRecurrence[{9,9,-1},{0,1,8},40] (* Harvey P. Dale, Aug 11 2013 *)

Formula

a(n)= (T(n, 5)-(-1)^n)/6, with Chebyshev's polynomials of the first kind evaluated at x=5: T(n, 5)=A001079(n)=((5+2*sqrt(6))^n + (5-2*sqrt(6))^n)/2.

a(n)= 10*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.

a(n)= 9*a(n-1) + 9*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=8.

G.f.: x*(1-x)/((1+x)*(1-10*x+x^2)) = x*(1-x)/(1-9*x-9*x^2+x^3) (from the Stephan link, see A092184).

a(x)=1/12(2*(-1)^x+(5+2*Sqrt[6])(5-2*Sqrt[6])^x+(5-2*Sqrt[6])(5+2*Sqrt[6])^x). - Harvey P. Dale, Aug 11 2013

a(n-1)+a(n) = A072256(n). - R. J. Mathar, Feb 19 2017