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Search: id:A013595
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| A013595 |
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Triangle of coefficients of cyclotomic polynomial Phi_n(x) (exponents in increasing order). |
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+0
8
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| 0, 1, -1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 0, 1, -1, 1, 0, -1, 1, 1, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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We follow Maple in defining Phi_0 to be x; it could equally well be taken to be 1.
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REFERENCES
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E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, 1968; see p. 90.
Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, p. 325.
K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer, 1982, p. 194.
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EXAMPLE
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Phi_0 = x; Phi_1 = x-1; Phi_2 = x+1; Phi_3 = x^2+x+1; Phi_4 = x^2+1; ...
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MAPLE
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with(numtheory): [ seq(cyclotomic(n, x), n=0..48) ];
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MATHEMATICA
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lst={}; Do[lst=Join[lst, CoefficientList[Cyclotomic[n, x], x]], {n, 0, 20}]; lst (T. D. Noe (noe(AT)sspectra.com), Dec 06 2005)
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CROSSREFS
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Cf. A013596.
Sequence in context: A022932 A079421 A164980 this_sequence A011582 A145568 A123927
Adjacent sequences: A013592 A013593 A013594 this_sequence A013596 A013597 A013598
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KEYWORD
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sign,easy,nice,tabf
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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