A099273 Unsigned member r=-15 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 15, 256, 4335, 73441, 1244160, 21077281, 357069615, 6049106176, 102477735375, 1736072395201, 29410752983040, 498246728316481, 8440783628397135, 142995074954434816, 2422475490596994735

Offset: 0

Author

Wolfdieter Lang, Oct 18 2004

Keywords

• nonn
• easy

Comments

((-1)^(n+1))*a(n) = S_{-15}(n), n>=0, defined in A092184.

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (16, 16, -1).

Programs

Mathematica

LinearRecurrence[{16,16,-1},{0,1,15},30] (* Harvey P. Dale, Oct 09 2011 *)

Formula

a(n)= 2*(T(n, 17/2)-(-1)^n)/19, with twice Chebyshev's polynomials of the first kind evaluated at x=17/2: 2*T(n, 17/2)=A078367(n)= ((17+sqrt(285))^n +(17-sqrt(285))^n)/2^n.

a(n)= 17*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.

a(n)= 16*a(n-1) + 16*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=15.

G.f.: x*(1-x)/((1+x)*(1-17*x+x^2)) = x*(1-x)/(1-16*x-16*x^2+x^3) (from the Stephan link, see A092184).