Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Nov 20 2022 14:43:23
%S 1,18,306,5185,87840,1488096,25209793,427078386,7235122770,
%T 122570008705,2076455025216,35177165419968,595935357114241,
%U 10095723905522130,171031371036761970,2897437583719431361,49085407552193571168
%N Partial sums of Chebyshev sequence S(n,17)= U(n,17/2)=A078366(n).
%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 (18,-18,1).
%F a(n) = sum(S(k, 17), k=0..n) with S(k, 17) = U(k, 17/2) = A078366(k) Chebyshev's polynomials of the second kind.
%F G.f.: 1/((1-x)*(1-17*x+x^2)) = 1/(1-18*x+18*x^2-x^3).
%F a(n) = 18*a(n-1)-18*a(n-2)+a(n-3), n>=2, a(-1)=0, a(0)=1, a(1)=18.
%F a(n) = 17*a(n-1)-a(n-2)+1, n>=1, a(-1)=0, a(0)=1.
%F a(n) = (S(n+1, 17) - S(n, 17) -1)/15.
%t LinearRecurrence[{18,-18,1},{1,18,306},20] (* _Harvey P. Dale_, Nov 20 2022 *)
%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