A099277 Unsigned member r=-19 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 19, 400, 8379, 175561, 3678400, 77070841, 1614809259, 33833923600, 708897586339, 14853015389521, 311204425593600, 6520439922076081, 136618033938004099, 2862458272776010000, 59975005694358205899

Offset

0,3

Comments

((-1)^(n+1))*a(n) = S_{-19}(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 (20, 20, -1).

Formula

a(n)= 2*(T(n, 21/2)-(-1)^n)/23, with twice Chebyshev's polynomials of the first kind evaluated at x=21/2: 2*T(n, 21/2)=A090729(n)= ((21+sqrt(437))^n + (21-sqrt(437))^n)/2^n.

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

a(n)= 20*a(n-1) + 20*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=19.

G.f.: x*(1-x)/((1+x)*(1-21*x+x^2)) = x*(1-x)/(1-20*x-20*x^2+x^3) (from the Stephan link, see A092184).

Crossrefs

Sequence in context: A009075 A221584 A015694 * A252927 A172740 A172816

Adjacent sequences: A099274 A099275 A099276 * A099278 A099279 A099280

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 18 2004

Status

approved