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A098309 Unsigned member r = -10 of the family of Chebyshev sequences S_r(n) defined in A092184. 1

%I #13 Oct 28 2019 15:40:01

%S 0,1,10,121,1440,17161,204490,2436721,29036160,345997201,4122930250,

%T 49129165801,585427059360,6975995546521,83126519498890,

%U 990542238440161,11803380341783040,140650021862956321,1675996882013692810,19971312562301357401,237979753865602596000

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

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

%H Colin Barker, <a href="/A098309/b098309.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,11,-1).

%F 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.

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

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

%F 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).

%F a(n) = (-2*(-1)^n + (6-sqrt(35))^n + (6+sqrt(35))^n) / 14. - _Colin Barker_, Jan 31 2017

%t LinearRecurrence[{11,11,-1},{0,1,10},30] (* _Harvey P. Dale_, Oct 28 2019 *)

%o (PARI) concat(0, Vec(x*(1-x)/(1-11*x-11*x^2+x^3) + O(x^30))) \\ _Colin Barker_, Jan 31 2017

%K nonn,easy

%O 0,3

%A _Wolfdieter Lang_, Oct 18 2004

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)