A099275 Unsigned member r=-17 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 17, 324, 6137, 116281, 2203200, 41744521, 790942697, 14986166724, 283946225057, 5379992109361, 101935903852800, 1931402181093841, 36594705536930177, 693368003020579524, 13137397351854080777

Offset

0,3

Comments

((-1)^(n+1))*a(n) = S_{-17}(n), n>=0, defined in A092184.

Links

Table of n, a(n) for n=0..16.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (18,18,-1).

Formula

a(n)= 2*(T(n, 19/2)-(-1)^n)/21, with twice Chebyshev's polynomials of the first kind evaluated at x=19/2: 2*T(n, 19/2)=A078369(n)= ((19+sqrt(357))^n + (19-sqrt(357))^n)/2^n.

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

a(n)= 18*a(n-1) + 18*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=17.

G.f.: x*(1-x)/((1+x)*(1-19*x+x^2)) = x*(1-x)/(1-18*x-18*x^2+x^3) (from the Stephan link, see A092184).

Crossrefs

Sequence in context: A091464 A015693 A029535 * A299706 A318597 A142933

Adjacent sequences: A099272 A099273 A099274 * A099276 A099277 A099278

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 18 2004

Status

approved