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)
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)=Coefficients(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
KEYWORD
tabf,uned,sign
AUTHOR
Roger L. Bagula and Gary W. Adamson, Jul 11 2008
STATUS
approved