A099271 Unsigned member r=-13 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 13, 196, 2925, 43681, 652288, 9740641, 145457325, 2172119236, 32436331213, 484372848961, 7233156403200, 108012973199041, 1612961441582413, 24086408650537156, 359683168316474925, 5371161116096586721

Offset: 0

Author

Wolfdieter Lang, Oct 18 2004

Keywords

• nonn
• easy

Comments

((-1)^(n+1))*a(n) = S_{-13}(n), n>=0, defined in A092184.

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (14, 14, -1).

Programs

Mathematica

LinearRecurrence[{14,14,-1},{0,1,13},41] (* or *) CoefficientList[Series[ (x-x^2)/(1-14 x-14 x^2+x^3),{x,0,40}],x] (* Harvey P. Dale, Jun 18 2011 *)

Formula

a(n)= 2*(T(n, 15/2)-(-1)^n)/17, with twice Chebyshev's polynomials of the first kind evaluated at x=15/2: 2*T(n, 15/2)=A078365(n)=((15+sqrt(221))^n + (15-sqrt(221))^n)/2^n.

a(n)= 15*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.

a(n)= 14*a(n-1) + 14*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=13.

G.f.: x*(1-x)/((1+x)*(1-15*x+x^2)) = x*(1-x)/(1-14*x-14*x^2+x^3) (from the Stephan link, see A092184).