A099272 Unsigned member r=-14 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 14, 225, 3584, 57121, 910350, 14508481, 231225344, 3685097025, 58730327054, 936000135841, 14917271846400, 237740349406561, 3788928318658574, 60385112749130625, 962372875667431424, 15337580897929772161, 244438921491208923150, 3895685162961412998241

Offset

0,3

Comments

((-1)^(n+1))*a(n) = S_{-14}(n), n>=0, defined in A092184.

Links

Robert Israel, Table of n, a(n) for n = 0..831

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (15, 15, -1).

Formula

a(n) = (T(n, 8)-(-1)^n)/9, with Chebyshev's polynomials of the first kind evaluated at x=8: T(n, 8)=A001081(n)=((8+3*sqrt(7))^n + (8-3*sqrt(7))^n)/2.

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

a(n) = 15*a(n-1) + 15*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=14.

G.f.: x*(1-x)/((1+x)*(1-16*x+x^2)) = x*(1-x)/(1-15*x-15*x^2+x^3) (from the Stephan link, see A092184).

Maple

f:= n -> (orthopoly[T](n, 8)-(-1)^n)/9:
map(f, [$0..20]); # Robert Israel, Jun 04 2018

Mathematica

CoefficientList[Series[x (1-x)/(1-15 x-15 x^2+x^3), {x, 0, 33}], x] (* Vincenzo Librandi, Jun 05 2018 *)

Crossrefs

Cf. A001081.

Sequence in context: A221582 A320762 A027774 * A273625 A120048 A079563

Adjacent sequences: A099269 A099270 A099271 * A099273 A099274 A099275

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 18 2004

Status

approved