A099278 Unsigned member r=-20 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 20, 441, 9680, 212521, 4665780, 102434641, 2248896320, 49373284401, 1083963360500, 23797820646601, 522468090864720, 11470500178377241, 251828535833434580, 5528757288157183521, 121380831803624602880

Offset: 0

Author

Wolfdieter Lang, Oct 18 2004

Keywords

• nonn
• easy

Comments

((-1)^(n+1))*a(n) = S_{-20}(n), n>=0, defined in A092184.

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (21, 21, -1).

Formula

a(n)= (T(n, 11)-(-1)^n)/12, with Chebyshev's polynomials of the first kind evaluated at x=11: T(n, 11)=A077422(n)=((11+2*sqrt(30))^n + (11-2*sqrt(30))^n)/2.

a(n)= 22*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.

a(n)= 21*a(n-1) + 21*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=20.

G.f.: x*(1-x)/((1+x)*(1-22*x+x^2)) = x*(1-x)/(1-21*x-21*x^2+x^3) (from the Stephan link, see A092184).