OFFSET
1,5
COMMENTS
Row sums are:
{1, 0, 4, 6, 8, 10, 16, 14, 32, 24, 64}.
The problem with Cyclotomic polynomials is there uneven lengths:
Here roots of -1 as (x+1) powers are used to fill out the triangle with positive coefficients.
FORMULA
p(x,n)=If[PrimeQ[n], Cyclotomic[n, x]*(x + 1), Cyclotomic[n, x]*(x + 1)^(n + 1 - Length[CoefficientList[Cyclotomic[n, x], x]])]; t(n,m)=Coefficients(p)x,n))
EXAMPLE
{1},
{-1, 1},
{1, 2, 1},
{1, 2, 2, 1},
{1, 2, 2, 2, 1},
{1, 2, 2, 2, 2, 1},
{1, 3, 3, 2, 3, 3, 1},
{1, 2, 2, 2, 2, 2, 2, 1},
{1, 4, 6, 4, 2, 4, 6, 4, 1},
{1, 3, 3, 2, 3, 3, 2, 3, 3, 1},
{1, 5, 10, 10, 5, 2, 5, 10, 10, 5, 1}
MATHEMATICA
p[x_, n_] := If[PrimeQ[n], Cyclotomic[n, x]*(x + 1), Cyclotomic[n, x]*(x + 1)^(n + 1 - Length[CoefficientList[Cyclotomic[n, x], x]])]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
CROSSREFS
KEYWORD
uned,sign
AUTHOR
Roger L. Bagula and Gary W. Adamson, Oct 20 2008
STATUS
approved