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Search: id:A095878
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| A095878 |
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Value of middle coefficient of the cyclotomic polynomial Phi_n(x) for n in A095877. |
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+0
2
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| 1, 0, -1, -3, 3, 5, -5, -7, 7, 19, -11, 25, 11, 27, -9, 9, 45, 13, -35, -15, -23, 17, 349, -65, -27, -17
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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After the second term, the entries are always odd; see Dresden's article for proof.
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REFERENCES
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G. Dresden, On the Middle Coefficient of the Cyclotomic Polynomial, MAA Monthly 111 (2004), 531--533.
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LINKS
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G. Dresden, On the Middle Coefficient of the Cyclotomic Polynomial (MAA Monthly, 2004, 531-533).
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MATHEMATICA
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vals={1, 0, -1}; lst={3, 4, 6}; Do[pwrs=Transpose[FactorInteger[n]][[2]]; If[Length[pwrs]>2 && 1==Times@@pwrs, c=Coefficient[Cyclotomic[n, x], x, EulerPhi[n]/2]; If[ !MemberQ[vals, c], AppendTo[lst, n]; AppendTo[vals, c]]], {n, 7, 50000, 2}]; vals
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CROSSREFS
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Cf. A094754 (middle coefficient of cyclotomic polynomial Phi_n(x)).
Sequence in context: A073737 A133908 A111213 this_sequence A077381 A139069 A087715
Adjacent sequences: A095875 A095876 A095877 this_sequence A095879 A095880 A095881
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KEYWORD
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hard,sign
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jun 10 2004
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