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A175629
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Legendre symbol (n,7).
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13
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0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1
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OFFSET
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0,1
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COMMENTS
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This represents a non-principal Dirichlet character modulo 7.
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1986, page 139, k=7, Chi_2(n).
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LINKS
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FORMULA
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a(n) = a(n+7).
a(n) = -a(n-1) - a(n-2) - a(n-3) - a(n-4) - a(n-5) - a(n-6).
G.f.: x*(1 + 2*x + x^2 + 2*x^3 + x^4)/(1 + x + x^2 + x^3 + x^4 + x^5 + x^6).
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MAPLE
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A := proc(n) numtheory[jacobi](n, 7) ; end proc: seq(A(n), n=0..120) ;
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MATHEMATICA
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LinearRecurrence[{-1, -1, -1, -1, -1, -1}, {0, 1, 1, -1, 1, -1}, 100] (* or *) PadRight[ {}, 100, {0, 1, 1, -1, 1, -1, -1}] (* Harvey P. Dale, Aug 02 2013 *)
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PROG
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CROSSREFS
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The Legendre symbols (n,p): A091337 (p = 2, Kronecker symbol), A102283 (p = 3), A080891 (p = 5), this sequence (p = 7), A011582 (p = 11), A011583 (p = 13), ..., A011631 (p = 251), A165573 (p = 257), A165574 (p = 263). Also, many other sequences for p > 263 are in the OEIS.
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KEYWORD
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easy,mult,sign
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AUTHOR
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STATUS
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approved
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