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A097784
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Partial sums of Chebyshev sequence S(n,10)= U(n,5)= A004189(n+1).
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9
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1, 11, 110, 1090, 10791, 106821, 1057420, 10467380, 103616381, 1025696431, 10153347930, 100507782870, 994924480771, 9848737024841, 97492445767640, 965075720651560, 9553264760747961, 94567571886828051, 936122454107532550
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OFFSET
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0,2
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REFERENCES
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D. Fortin, B-SPLINE TOEPLITZ INVERSE UNDER CORNER PERTURBATIONS, International Journal of Pure and Applied Mathematics, Volume 77, No. 1, 2012, 107-118; http://ijpam.eu/contents/2012-77-1/11/11.pdf. - From N. J. A. Sloane, Oct 22 2012
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LINKS
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Table of n, a(n) for n=0..18.
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n) = sum(S(k, 10), k=0..n) with S(k, 10) = U(k, 5) = A004189(k+1) Chebyshev's polynomials of the second kind.
G.f.: 1/((1-x)*(1-10*x+x^2)) = 1/(1-11*x+11*x^2-x^3).
a(n) = 11*a(n-1)-11*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=11.
a(n) = 10*a(n-1)-a(n-2)+1 with n>=1, a(-1)=0, a(0)=1.
a(n) = (S(n+1, 10) - S(n, 10) -1)/8.
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MATHEMATICA
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Join[{a=1, b=11}, Table[c=10*b-a+1; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 20 2011*)
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CROSSREFS
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Cf. A098296.
Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3).
Sequence in context: A115822 A162760 A190871 * A121031 A115804 A162987
Adjacent sequences: A097781 A097782 A097783 * A097785 A097786 A097787
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Aug 31 2004
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STATUS
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approved
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