A097831 Partial sums of Chebyshev sequence S(n,17)= U(n,17/2)=A078366(n).

1, 18, 306, 5185, 87840, 1488096, 25209793, 427078386, 7235122770, 122570008705, 2076455025216, 35177165419968, 595935357114241, 10095723905522130, 171031371036761970, 2897437583719431361, 49085407552193571168

Offset: 0

Author

Wolfdieter Lang, Aug 31 2004

Keywords

• nonn
• easy

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (18,-18,1).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{18,-18,1},{1,18,306},20] (* Harvey P. Dale, Nov 20 2022 *)

Formula

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.

G.f.: 1/((1-x)*(1-17*x+x^2)) = 1/(1-18*x+18*x^2-x^3).

a(n) = 18*a(n-1)-18*a(n-2)+a(n-3), n>=2, a(-1)=0, a(0)=1, a(1)=18.

a(n) = 17*a(n-1)-a(n-2)+1, n>=1, a(-1)=0, a(0)=1.

a(n) = (S(n+1, 17) - S(n, 17) -1)/15.