A097829 Partial sums of Chebyshev sequence S(n,15)= U(n,15/2)=A078364(n).

1, 16, 240, 3585, 53536, 799456, 11938305, 178275120, 2662188496, 39754552321, 593656096320, 8865086892480, 132382647290881, 1976874622470736, 29520736689770160, 440834175724081665, 6582991899171454816

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 (16, -16, 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, 15), k=0..n) with S(k, 15) = U(k, 15/2) = A078364(k) Chebyshev's polynomials of the second kind.

G.f.: 1/((1-x)*(1-15*x+x^2)) = 1/(1-16*x+16*x^2-x^3).

a(n) = 16*a(n-1)-16*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=16.

a(n) = 15*a(n-1)-a(n-2)+1 with n>=1, a(-1)=0, a(0)=1.

a(n) = (S(n+1, 15) - S(n, 15) -1)/13.