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A140666
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A triangle of coefficients of the difference of prime cyclotomic doubled polynomials: p(x,n)=(c(x,Prime[n])-c(x,2*Prime[n]))/x.
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0
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1, -1, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums are: {0, 2, 4, 6, 10, 12, 16, 18, 22, 28, ...}
The factor x is used instead of 2x to get an integer n=1 term.
p(x,n)/2 are related to the double product:two primes n,m such that
Cyclotomic[Prime[n], x]* Cyclotomic[2*Prime[n]=(Cyclotomic[Prime[m], x] - Cyclotomic[2*Prime[m], x])/(2*x)
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FORMULA
| c(x,n)=CyclotomicPolynomial; c(x,Prime[n])=(x^Prime[n]-1)/(x-1); p(x,n)=(c(x,Prime[n])-c(x,2*Prime[n]))/x; a(n,m)=Coefficiencts(p(x,n))
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EXAMPLE
| {1, -1},
{2},
{2, 0, 2},
{2, 0, 2, 0, 2},
{2, 0, 2, 0, 2, 0, 2, 0, 2},
{2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2},
{2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2},
{2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2},
{2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2},
{2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2}
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MATHEMATICA
| Clear[p, x, n] p[x_, n_] = (Cyclotomic[Prime[n], x] - Cyclotomic[2*Prime[n], x])/x; Table[ExpandAll[p[x, n]], {n, 1, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 1, 10}]; Flatten[a]
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CROSSREFS
| Sequence in context: A045719 A114906 A114700 * A202145 A130772 A109265
Adjacent sequences: A140663 A140664 A140665 * A140667 A140668 A140669
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KEYWORD
| tabl,uned,sign
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 11 2008
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