A098309 Unsigned member r = -10 of the family of Chebyshev sequences S_r(n) defined in A092184.

0, 1, 10, 121, 1440, 17161, 204490, 2436721, 29036160, 345997201, 4122930250, 49129165801, 585427059360, 6975995546521, 83126519498890, 990542238440161, 11803380341783040, 140650021862956321, 1675996882013692810, 19971312562301357401, 237979753865602596000

Offset

0,3

Comments

((-1)^(n+1))*a(n) = S_{-10}(n), n>=0, defined in A092184.

Links

Colin Barker, Table of n, a(n) for n = 0..900

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (11,11,-1).

Formula

a(n) = (T(n, 6)-(-1)^n)/7, with Chebyshev's polynomials of the first kind evaluated at x=6: T(n, 6)=A023038(n)=((6+sqrt(35))^n + (6-sqrt(35))^n)/2.

a(n) = 12*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.

a(n) = 11*a(n-1) + 11*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=10.

G.f.: x*(1-x)/((1+x)*(1-12*x+x^2)) = x*(1-x)/(1-11*x-11*x^2+x^3) (from the Stephan link, see A092184).

a(n) = (-2*(-1)^n + (6-sqrt(35))^n + (6+sqrt(35))^n) / 14. - Colin Barker, Jan 31 2017

Mathematica

LinearRecurrence[{11, 11, -1}, {0, 1, 10}, 30] (* Harvey P. Dale, Oct 28 2019 *)

Prog

(PARI) concat(0, Vec(x*(1-x)/(1-11*x-11*x^2+x^3) + O(x^30))) \\ Colin Barker, Jan 31 2017

Crossrefs

Sequence in context: A330847 A202808 A091692 * A056116 A246643 A233084

Adjacent sequences: A098306 A098307 A098308 * A098310 A098311 A098312

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 18 2004

Status

approved