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Search: id:A097828
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| A097828 |
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Partial sums of Chebyshev sequence S(n,13)= U(n,13/2)=A078362(n). |
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+0
4
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| 1, 14, 182, 2353, 30408, 392952, 5077969, 65620646, 847990430, 10958254945, 141609323856, 1829962955184, 23647909093537, 305592855260798, 3949059209296838, 51032176865598097, 659469240043478424
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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, 13), k=0..n) with S(k, 13)=U(k, 13/2)=A078362(k) Chebyshev's polynomials of the second kind.
G.f.: 1/((1-x)*(1-13*x+x^2)) = 1/(1-14*x+14*x^2-x^3).
a(n)=14*a(n-1)-14*a(n-2)+a(n-3), n>=2, a(-1):=0, a(0)=1, a(1)=14.
a(n)=13*a(n-1)-a(n-2)+1, n>=1, a(-1):=0, a(0)=1.
a(n)=(S(n+1, 13) - S(n, 13) -1)/11.
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CROSSREFS
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Adjacent sequences: A097825 A097826 A097827 this_sequence A097829 A097830 A097831
Sequence in context: A132010 A126866 A133286 this_sequence A030008 A091030 A055759
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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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