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A234046
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Period 7: repeat [0, 1, -1, 0, 0, -1, 1].
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5
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0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1
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OFFSET
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0
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COMMENTS
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This is the sequence called c(n) in A234044 used in a formula for 2*exp(2*Pi*n*I/7) together with five other sequences: a(n) = A234044(n), b(n) = A234045(n), A(n) = A238468(n), B(n) = A238469(n) and C(n) = A238470(n). An example for n=4 is also given there.
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LINKS
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Table of n, a(n) for n=0..90.
Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1,-1,-1).
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FORMULA
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G.f.: x*(1 - x - x^4 + x^5)/(1 - x^7).
a(n+7) = a(n), n>=0, with a(0) = a(3) = a(4) = 0 and a(1) = -a(2) = -a(5) = a(6) = 1.
From Wesley Ivan Hurt, Jul 19 2016: (Start)
a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) = 0 for n>5.
a(n) = - floor(n/7) + 2*floor((1+n)/7) - floor((2+n)/7) + floor((4+n)/7) - 2*floor((5+n)/7) + floor((6+n)/7). (End)
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MAPLE
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seq(op([0, 1, -1, 0, 0, -1, 1]), n=0..20); # Wesley Ivan Hurt, Jul 19 2016
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MATHEMATICA
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PadRight[{}, 100, {0, 1, -1, 0, 0, -1, 1}] (* Wesley Ivan Hurt, Jul 19 2016 *)
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PROG
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(MAGMA) &cat [[0, 1, -1, 0, 0, -1, 1]^^20]; // Wesley Ivan Hurt, Jul 19 2016
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CROSSREFS
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Cf. A234044, A234045, A238468, A238469, A238470.
Sequence in context: A269927 A246146 A191162 * A285565 A188076 A189011
Adjacent sequences: A234043 A234044 A234045 * A234047 A234048 A234049
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KEYWORD
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sign,easy
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AUTHOR
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Wolfdieter Lang, Feb 27 2014
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STATUS
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approved
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