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 A097827 Partial sums of Chebyshev sequence S(n,12)= U(n,6)=A004191(n). 0

%I

%S 1,13,156,1860,22165,264121,3147288,37503336,446892745,5325209605,

%T 63455622516,756142260588,9010251504541,107366875793905,

%U 1279392258022320,15245340220473936,181664690387664913

%N Partial sums of Chebyshev sequence S(n,12)= U(n,6)=A004191(n).

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

%F a(n) = sum(S(k, 12), k=0..n) with S(k, 12) = U(k, 6) = A004191(k) Chebyshev's polynomials of the second kind.

%F G.f.: 1/((1-x)*(1-12*x+x^2)) = 1/(1-13*x+13*x^2-x^3).

%F a(n) = 13*a(n-1)-13*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=13.

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

%F a(n) = (S(n+1, 12) - S(n, 12) -1)/10.

%Y Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3).

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Aug 31 2004

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Last modified October 16 06:21 EDT 2019. Contains 328048 sequences. (Running on oeis4.)