A099276 Unsigned member r=-18 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 18, 361, 7200, 143641, 2865618, 57168721, 1140508800, 22753007281, 453919636818, 9055639729081, 180658874944800, 3604121859166921, 71901778308393618, 1434431444308705441, 28616727107865715200

Offset: 0

Author

Wolfdieter Lang, Oct 18 2004

Keywords

• nonn
• easy

Comments

((-1)^(n+1))*a(n) = S_{-18}(n), n>=0, defined in A092184.

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (19,19,-1)>

Programs

Mathematica

LinearRecurrence[{19,19,-1},{0,1,18},30] (* Harvey P. Dale, Sep 08 2024 *)

Formula

a(n)= 20*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.

a(n)= 19*a(n-1) + 19*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=18.

G.f.: x*(1-x)/((1+x)*(1-20*x+x^2)) = x*(1-x)/(1-19*x-19*x^2+x^3) (from the Stephan link, see A092184).

a(n)= (T(n, 10)-(-1)^n)/11, with Chebyshev's polynomials of the first kind evaluated at x=10: T(n, 10)=A001085(n)=((10+3*sqrt(11))^n + (10-3*sqrt(11))^n)/2.