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A057086
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Scaled Chebyshev U-polynomials evaluated at sqrt(10)/2.
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12
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1, 10, 90, 800, 7100, 63000, 559000, 4960000, 44010000, 390500000, 3464900000, 30744000000, 272791000000, 2420470000000, 21476790000000, 190563200000000, 1690864100000000, 15003009000000000, 133121449000000000, 1181184400000000000, 10480629510000000000
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OFFSET
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0,2
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COMMENTS
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The characteristic roots are rp(m) := (m + sqrt(m*(m-4)))/2 and rm(m) := (m-sqrt(m*(m-4)))/2 and a(n,m)= (rp(m)^(n+1) - rm(m)^(n+1))/(rp(m) - rm(m)) is the Binet form of these m-sequences.
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LINKS
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FORMULA
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a(n) = 10*(a(n-1) - a(n-2)), a(-1)=0, a(0)=1.
a(n) = S(n, sqrt(10))*(sqrt(10))^n with S(n, x) := U(n, x/2), Chebyshev's polynomials of the 2nd kind, A049310.
G.f.: 1/(1-10*x+10*x^2).
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MATHEMATICA
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PROG
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(Sage) [lucas_number1(n, 10, 10) for n in range(1, 20)] # Zerinvary Lajos, Apr 26 2009
(PARI) Vec(1/(1-10*x+10*x^2) + O(x^30)) \\ Colin Barker, Jun 14 2015
(Magma) [(10)^n*Evaluate(DicksonSecond(n, 1/10), 1): n in [0..30]]; # G. C. Greubel, May 02 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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