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A274220
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a(n) = (-cos(Pi/7)/cos(2*Pi/7))^n + (-cos(2*Pi/7)/cos(3*Pi/7))^n + (cos(3*Pi/7)/cos(Pi/7))^n.
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6
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3, -4, 10, -25, 66, -179, 493, -1369, 3818, -10672, 29865, -83626, 234237, -656205, 1838483, -5151080, 14432666, -40438941, 113306686, -317477255, 889550021, -2492461633, 6983719214, -19567941936, 54828148469, -153625048854, 430447808073, -1206087937261, 3379383275971, -9468821484028
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OFFSET
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0,1
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COMMENTS
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a(n) is an integer.
a(n) is the sum of n-th powers of the roots of x^3 + 4*x^2 + 3*x - 1. - Greg Dresden, Mar 11 2020
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REFERENCES
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R. Witula, E. Hetmaniok, D. Slota, Sums of the powers of any order roots taken from the roots of a given polynomial, Proceedings of the Fifteenth International Conference on Fibonacci Numbers and Their Applications, Eger, Hungary, 2012.
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LINKS
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FORMULA
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a(n) = -4*a(n-1)-3*a(n-2)+a(n-3).
G.f.: (3+8*x+3*x^2) / (1+4*x+3*x^2-x^3). - Colin Barker, Jun 14 2016
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EXAMPLE
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a(0) = 3, a(1) = -4, a(2) = 10, a(3) = -25.
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MATHEMATICA
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CoefficientList[Series[(3 + 8 x + 3 x^2)/(1 + 4 x + 3 x^2 - x^3), {x, 0, 29}], x] (* Michael De Vlieger, Jun 14 2016 *)
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PROG
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(PARI) Vec((3+8*x+3*x^2)/(1+4*x+3*x^2-x^3) + O(x^30)) \\ Colin Barker, Jun 14 2016
(PARI) polsym(x^3 + 4*x^2 + 3*x - 1, 33) \\ Joerg Arndt, Mar 12 2020
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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