A097830 Partial sums of Chebyshev sequence S(n,16) = U(n,16/2) = A077412(n).

1, 17, 272, 4336, 69105, 1101345, 17552416, 279737312, 4458244577, 71052175921, 1132376570160, 18046972946640, 287619190576081, 4583860076270657, 73054142029754432, 1164282412399800256, 18555464456367049665, 295723148889472994385, 4713014917775200860496

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..800

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (17, -17, 1).

Formula

a(n) = sum(S(k, 16), k=0..n) with S(k, 16) = U(k, 8) = A077412(k) Chebyshev's polynomials of the second kind.

G.f.: 1/((1-x)*(1-16*x+x^2)) = 1/(1-17*x+17*x^2-x^3).

a(n) = 17*a(n-1)-17*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=17.

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

a(n) = (S(n+1, 16) - S(n, 16) -1)/14.

a(n) = (-6+(45-17*sqrt(7))*(8-3*sqrt(7))^n+(8+3*sqrt(7))^n*(45+17*sqrt(7)))/84. - Colin Barker, Mar 04 2016

Mathematica

LinearRecurrence[{17, -17, 1}, {1, 17, 272}, 30] (* or *) Accumulate[ ChebyshevU[Range[0, 30], 8]] (* Harvey P. Dale, Nov 09 2011 *)

Prog

(PARI) Vec(1/((1-x)*(1-16*x+x^2)) + O(x^25)) \\ Colin Barker, Mar 04 2016

Crossrefs

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

Sequence in context: A142898 A159678 A162803 * A163093 A163451 A163965

Adjacent sequences: A097827 A097828 A097829 * A097831 A097832 A097833

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 31 2004

Status

approved