A097832 Partial sums of Chebyshev sequence S(n,19)= U(n,19/2)=A078368(n).

1, 20, 380, 7201, 136440, 2585160, 48981601, 928065260, 17584258340, 333172843201, 6312699762480, 119608122643920, 2266241630472001, 42938982856324100, 813574432639685900, 15414975237297708001

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 (20, -20, 1).

Crossrefs

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

Formula

a(n) = sum(S(k, 19), k=0..n) with S(k, 19) = U(k, 19/2) = A078368(k) Chebyshev's polynomials of the second kind.

G.f.: 1/((1-x)*(1-19*x+x^2)) = 1/(1-20*x+20*x^2-x^3).

a(n) = 20*a(n-1)-20*a(n-2)+a(n-3), n>=2, a(-1)=0, a(0)=1, a(1)=20.

a(n) = 19*a(n-1)-a(n-2)+1, n>=1, a(-1)=0, a(0)=1.

a(n) = (S(n+1, 19) - S(n, 19) -1)/17.