A097828 Partial sums of Chebyshev sequence S(n,13)= U(n,13/2) = A078362(n).

1, 14, 182, 2353, 30408, 392952, 5077969, 65620646, 847990430, 10958254945, 141609323856, 1829962955184, 23647909093537, 305592855260798, 3949059209296838, 51032176865598097, 659469240043478424, 8522067943699621416, 110127414028051599985, 1423134314420971178390

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (14,-14,1).

Index entries for sequences related to Chebyshev polynomials.

Formula

a(n) = Sum_{k=0..n} S(k, 13), with S(k, 13) = U(k, 13/2) = A078362(k) Chebyshev's polynomials of the second kind.

G.f.: 1/((1-x)*(1-13*x+x^2)) = 1/(1-14*x+14*x^2-x^3).

a(n) = 14*a(n-1)-14*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=14.

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

a(n) = (S(n+1, 13) - S(n, 13) - 1)/11.

Sum_{n>=0} 1/a(n) = (15 - sqrt(165))/2. - Amiram Eldar, Jan 31 2026

Mathematica

LinearRecurrence[{14, -14, 1}, {1, 14, 182}, 17] (* Amiram Eldar, Jan 31 2026 *)

Crossrefs

Cf. A078362.

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

Sequence in context: A163416 A162783 A199942 * A030008 A342883 A163090

Adjacent sequences: A097825 A097826 A097827 * A097829 A097830 A097831

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 31 2004

Status

approved