

A097830


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


2



1, 17, 272, 4336, 69105, 1101345, 17552416, 279737312, 4458244577, 71052175921, 1132376570160, 18046972946640, 287619190576081, 4583860076270657, 73054142029754432, 1164282412399800256, 18555464456367049665
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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/((1x)*(116*x+x^2)) = 1/(117*x+17*x^2x^3).
a(n) = 17*a(n1)17*a(n2)+a(n3) with n>=2, a(1)=0, a(0)=1, a(1)=17.
a(n) = 16*a(n1)a(n2)+1 with n>=1, a(1)=0, a(0)=1.
a(n) = (S(n+1, 16)  S(n, 16) 1)/14.


MATHEMATICA

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


CROSSREFS

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



