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A094754 Middle coefficient of cyclotomic polynomial Phi_n(x). 3


%S 0,0,1,0,1,-1,1,0,1,1,1,-1,1,-1,-1,0,1,-1,1,1,1,-1,1,-1,1,1,1,-1,1,-1,

%T 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,-1,1,1,1,

%U -1,1,-1,1,0,-1,-1,1,1,-1,1,1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,-1,1,1,-1

%N Middle coefficient of cyclotomic polynomial Phi_n(x).

%C a(n) = 0 if n is a power of 2, otherwise a(n) is odd.

%H T. D. Noe, <a href="/A094754/b094754.txt">Table of n, a(n) for n=1..10000</a>

%H G. P. Dresden, <a href="http://www.jstor.org/stable/4145075">On the middle coefficient of a cyclotomic polynomial</a>, Amer. Math. Monthly, 111 (No. 6, 2004), 531-533.

%p with(numtheory); t1:=[0,0]; for n from 3 to 120 do t2:=cyclotomic(n, x); t3:=degree(t2, x); t1:=[op(t1),coeff(t2, x,floor(t3/2))]; od: t1;

%Y Cf. A095877 (n such that the middle coefficient of Phi_n(x) has a value not obtained for smaller n).

%K sign

%O 1,1

%A _N. J. A. Sloane_, Jun 10 2004

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Last modified September 25 18:20 EDT 2017. Contains 292499 sequences.