A098307 Unsigned member r=-7 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 7, 64, 567, 5041, 44800, 398161, 3538647, 31449664, 279508327, 2484125281, 22077619200, 196214447521, 1743852408487, 15498457228864, 137742262651287, 1224181906632721, 10879894897043200, 96694872166756081

Offset: 0

Author

Wolfdieter Lang, Oct 18 2004

Keywords

• nonn
• easy

Comments

((-1)^(n+1))*a(n) = S_{-7}(n), n>=0, defined in A092184.

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (8,8,-1).

Programs

Mathematica

LinearRecurrence[{8,8,-1},{0,1,7},20] (* Harvey P. Dale, Jan 01 2017 *)

Formula

a(n)= 2*(T(n, 9/2)-(-1)^n)/11, with twice Chebyshev's polynomials of the first kind evaluated at x=9/2: 2*T(n, 9/2)=A056918(n)=((9+sqrt(77))^n + (9-sqrt(77))^n)/2^n.

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

a(n)= 8*a(n-1) + 8*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=7.

G.f.: x*(1-x)/((1+x)*(1-9*x+x^2)) = x*(1-x)/(1-8*x-8*x^2+x^3) (from the Stephan link, see A092184).