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Partial sums of Chebyshev sequence S(n,20)= U(n,10)=A075843(n+1).
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%I #14 Mar 03 2016 13:53:30

%S 1,21,420,8380,167181,3335241,66537640,1327417560,26481813561,

%T 528308853661,10539695259660,210265596339540,4194772231531141,

%U 83685179034283281,1669508808454134480,33306490990048406320

%N Partial sums of Chebyshev sequence S(n,20)= U(n,10)=A075843(n+1).

%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 (21, -21, 1).

%F a(n) = sum(S(k, 20), k=0..n) with S(k, 20) = U(k, 10) = A075843(k+1) Chebyshev's polynomials of the second kind.

%F G.f.: 1/((1-x)*(1-20*x+x^2)) = 1/(1-21*x+21*x^2-x^3).

%F a(n) = 20*a(n-1)-a(n-2)+1, n>=1, a(-1)=0, a(0)=1.

%F a(n) = (S(n+1, 20) - S(n, 20) -1)/18.

%F a(n) = 21*a(n-1)-21*a(n-2)+a(n-3), n>=2, a(-1)=0, a(0)=1, a(1)=21.

%F a(n) = (((10+3*sqrt(11))^(-n)*(33+10*sqrt(11)-11*(10+3*sqrt(11))^n*(1257+379*sqrt(11))+(10+3*sqrt(11))^(2*n)*(262680+79201*sqrt(11)))))/(198*(1257+379*sqrt(11))). - _Colin Barker_, Mar 03 2016

%t LinearRecurrence[{21, -21, 1},{1, 21, 420},16] (* _Ray Chandler_, Aug 11 2015 *)

%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