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%I #13 Feb 19 2017 12:52:43
%S 0,1,8,81,800,7921,78408,776161,7683200,76055841,752875208,7452696241,
%T 73774087200,730288175761,7229107670408,71560788528321,
%U 708378777612800,7012226987599681,69413891098384008,687126683996240401
%N Unsigned member r=-8 of the family of Chebyshev sequences S_r(n) defined in A092184.
%C ((-1)^(n+1))*a(n) = S_{-8}(n), n>=0, defined in A092184.
%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 (9,9,-1).
%F a(n)= (T(n, 5)-(-1)^n)/6, with Chebyshev's polynomials of the first kind evaluated at x=5: T(n, 5)=A001079(n)=((5+2*sqrt(6))^n + (5-2*sqrt(6))^n)/2.
%F a(n)= 10*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
%F a(n)= 9*a(n-1) + 9*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=8.
%F G.f.: x*(1-x)/((1+x)*(1-10*x+x^2)) = x*(1-x)/(1-9*x-9*x^2+x^3) (from the Stephan link, see A092184).
%F a(x)=1/12(2*(-1)^x+(5+2*Sqrt[6])(5-2*Sqrt[6])^x+(5-2*Sqrt[6])(5+2*Sqrt[6])^x). - _Harvey P. Dale_, Aug 11 2013
%F a(n-1)+a(n) = A072256(n). - _R. J. Mathar_, Feb 19 2017
%t LinearRecurrence[{9,9,-1},{0,1,8},40] (* _Harvey P. Dale_, Aug 11 2013 *)
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, Oct 18 2004
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