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, 2164730944431505021, 25795106642790395340, 307376548769053239060

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (13,-13,1).

Index entries for sequences related to Chebyshev polynomials.

Formula

a(n) = Sum_{k=0..n} S(k, 12), 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.

Sum_{n>=0} 1/a(n) = 7 - sqrt(35). - Amiram Eldar, Jan 31 2026

Mathematica

LinearRecurrence[{13, -13, 1}, {1, 13, 156}, 20] (* Amiram Eldar, Jan 31 2026 *)

Crossrefs

Cf. A004191.

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

Sequence in context: A297454 A102146 A162768 * A163084 A163438 A163958

Adjacent sequences: A097824 A097825 A097826 * A097828 A097829 A097830

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 31 2004

Status

approved