A098310 Unsigned member r=-11 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 11, 144, 1859, 24025, 310464, 4012009, 51845651, 669981456, 8657913275, 111882891121, 1445819671296, 18683772835729, 241443227193179, 3120078180675600, 40319573121589619, 521034372399989449

Offset: 0

Author

Wolfdieter Lang, Oct 18 2004

Keywords

• nonn
• easy

Comments

((-1)^(n+1))*a(n) = S_{-11}(n), n>=0, defined in A092184.

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (12,12,-1).

Programs

Mathematica

LinearRecurrence[{12,12,-1},{0,1,11},30] (* Harvey P. Dale, Mar 20 2023 *)

Formula

a(n)= 2*(T(n, 13/2)-(-1)^n)/15, with twice Chebyshev's polynomials of the first kind evaluated at x=13/2: 2*T(n, 13/2)=A078363(n)=((13+sqrt(165))^n + (13-sqrt(165))^n)/2^n.

a(n)= 13*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.

a(n)= 12*a(n-1) + 12*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=11.

G.f.: x*(1-x)/((1+x)*(1-13*x+x^2)) = x*(1-x)/(1-12*x-12*x^2+x^3) (from the Stephan link, see A092184).