%I #20 Mar 04 2016 08:31:16

%S 1,17,272,4336,69105,1101345,17552416,279737312,4458244577,

%T 71052175921,1132376570160,18046972946640,287619190576081,

%U 4583860076270657,73054142029754432,1164282412399800256,18555464456367049665,295723148889472994385,4713014917775200860496

%N Partial sums of Chebyshev sequence S(n,16) = U(n,16/2) = A077412(n).

%H Harvey P. Dale, <a href="/A097830/b097830.txt">Table of n, a(n) for n = 0..800</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 (17, -17, 1).

%F a(n) = sum(S(k, 16), k=0..n) with S(k, 16) = U(k, 8) = A077412(k) Chebyshev's polynomials of the second kind.

%F G.f.: 1/((1-x)*(1-16*x+x^2)) = 1/(1-17*x+17*x^2-x^3).

%F a(n) = 17*a(n-1)-17*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=17.

%F a(n) = 16*a(n-1)-a(n-2)+1 with n>=1, a(-1)=0, a(0)=1.

%F a(n) = (S(n+1, 16) - S(n, 16) -1)/14.

%F a(n) = (-6+(45-17*sqrt(7))*(8-3*sqrt(7))^n+(8+3*sqrt(7))^n*(45+17*sqrt(7)))/84. - _Colin Barker_, Mar 04 2016

%t LinearRecurrence[{17,-17,1},{1,17,272},30] (* or *) Accumulate[ ChebyshevU[Range[0,30],8]] (* _Harvey P. Dale_, Nov 09 2011 *)

%o (PARI) Vec(1/((1-x)*(1-16*x+x^2)) + O(x^25)) \\ _Colin Barker_, Mar 04 2016

%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