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A274032
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Sum of n-th powers of the roots of x^3 + 9*x^2 - x - 1.
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8
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3, -9, 83, -753, 6851, -62329, 567059, -5159009, 46935811, -427014249, 3884905043, -35344223825, 321555905219, -2925462465753, 26615373873171, -242142271419073, 2202970354179075, -20042260085157577, 182341168849178195, -1658909809373582257
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OFFSET
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0,1
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COMMENTS
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A Berndt-type sequence for tan(2*Pi/7).
a(n) is always an integer.
a(n) is x1^n + x2^n + x3^n, where x1, x2, x3 are the roots of the polynomial
x^3 + 9*x^2 - x - 1.
x1 = tan(Pi/7)/tan(2*Pi/7),
x2 = tan(2*Pi/7)/tan(4*Pi/7),
x3 = tan(4*Pi/7)/tan(Pi/7).
This is a two sided sequence. The other half is A274075. - Kai Wang, Aug 02 2016
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LINKS
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FORMULA
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a(n) = (tan(Pi/7)/tan(2*Pi/7))^n + (-tan(2*Pi/7)/tan(3*Pi/7))^n + (-tan(3*Pi/7)/tan(Pi/7))^n.
a(n) = -9*a(n-1)+a(n-2)+a(n-3) for n>2.
G.f.: (3+18*x-x^2) / (1+9*x-x^2-x^3).
(End)
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PROG
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(PARI) Vec((3+18*x-x^2)/(1+9*x-x^2-x^3) + O(x^30)) \\ Colin Barker, Jun 07 2016
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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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