A097827 Partial sums of Chebyshev sequence S(n,12)= U(n,6)=A004191(n).

1, 13, 156, 1860, 22165, 264121, 3147288, 37503336, 446892745, 5325209605, 63455622516, 756142260588, 9010251504541, 107366875793905, 1279392258022320, 15245340220473936, 181664690387664913

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 (13, -13, 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, 12), k=0..n) with S(k, 12) = U(k, 6) = A004191(k) Chebyshev's polynomials of the second kind.

G.f.: 1/((1-x)*(1-12*x+x^2)) = 1/(1-13*x+13*x^2-x^3).

a(n) = 13*a(n-1)-13*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=13.

a(n) = 12*a(n-1)-a(n-2)+1 with n>=1, a(-1)=0, a(0)=1.

a(n) = (S(n+1, 12) - S(n, 12) -1)/10.