

A140666


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.


0



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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OFFSET

1,3


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)


LINKS

Table of n, a(n) for n=1..111.


FORMULA

c(x,n)=CyclotomicPolynomial; c(x,Prime[n])=(x^Prime[n]1)/(x1); p(x,n)=(c(x,Prime[n])c(x,2*Prime[n]))/x; a(n,m)=Coefficiencts(p(x,n))


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}


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]


CROSSREFS

Sequence in context: A229723 A215879 A114700 * A202145 A130772 A109265
Adjacent sequences: A140663 A140664 A140665 * A140667 A140668 A140669


KEYWORD

tabf,uned,sign


AUTHOR

Roger L. Bagula and Gary W. Adamson, Jul 11 2008


STATUS

approved



