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Search: id:A097827
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| A097827 |
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Partial sums of Chebyshev sequence S(n,12)= U(n,6)=A004191(n). |
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1
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| 1, 13, 156, 1860, 22165, 264121, 3147288, 37503336, 446892745, 5325209605, 63455622516, 756142260588, 9010251504541, 107366875793905, 1279392258022320, 15245340220473936, 181664690387664913
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OFFSET
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0,2
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LINKS
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Index entries for sequences relate d to Chebyshev polynomials.
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FORMULA
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a(n)= sum(S(k, 12), k=0..n) 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), n>=2, a(-1):=0, a(0)=1, a(1)=13.
a(n)=12*a(n-1)-a(n-2)+1, n>=1, a(-1):=0, a(0)=1.
a(n)=(S(n+1, 12) - S(n, 12) -1)/10.
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CROSSREFS
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Sequence in context: A163415 A077416 A102146 this_sequence A142104 A140020 A130868
Adjacent sequences: A097824 A097825 A097826 this_sequence A097828 A097829 A097830
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004
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