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A097830
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Partial sums of Chebyshev sequence S(n,16)= U(n,16/2)= A077412(n).
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2
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1, 17, 272, 4336, 69105, 1101345, 17552416, 279737312, 4458244577, 71052175921, 1132376570160, 18046972946640, 287619190576081, 4583860076270657, 73054142029754432, 1164282412399800256, 18555464456367049665
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Index entries for sequences relate d to Chebyshev polynomials.
Harvey P. Dale, Table of n, a(n) for n = 0..800
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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), n>=2, a(-1):=0, a(0)=1, a(1)=17.
a(n)=16*a(n-1)-a(n-2)+1, n>=1, a(-1):=0, a(0)=1.
a(n)=(S(n+1, 16) - S(n, 16) -1)/14.
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MATHEMATICA
| LinearRecurrence[{17, -17, 1}, {1, 17, 272}, 30] (* or *) Accumulate[ ChebyshevU[Range[0, 30], 8]] (* From Harvey P. Dale, Nov 09 2011 *)
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CROSSREFS
| Sequence in context: A142898 A159678 A162803 * A163093 A163451 A163965
Adjacent sequences: A097827 A097828 A097829 * A097831 A097832 A097833
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004
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