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A142720
A triangle sequence of coefficients of odd sum polynomials: p(x,n)=x^(2*n - 1) - Sum[x^(2*i + 1), {i, 0, n - 1}] - 1.
0
-1, -1, -1, -1, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1
OFFSET
1,1
COMMENTS
Row sums are:
{-1, -2, -3, -4, -5, -6, -7, -8, -9, -10}.
FORMULA
p(x,n)=x^(2*n - 1) - Sum[x^(2*i + 1), {i, 0, n - 1}] - 1; t(n,m)=coefficients(p)x,n).
EXAMPLE
{-1},
{-1, -1},
{-1, -1, 0, -1},
{-1, -1, 0, -1, 0, -1},
{-1, -1, 0, -1, 0, -1, 0, -1},
{-1, -1, 0, -1, 0, -1, 0, -1, 0, -1},
{-1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1},
{-1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1},
{-1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1},
{-1, -1, 0, -1, 0, -1, 0, -1, 0, -1,0, -1, 0, -1, 0, -1, 0, -1}
MATHEMATICA
p[x_, n_] := x^(2*n - 1) - Sum[x^(2*i + 1), {i, 0, n - 1}] - 1; Table[Expand[p[x, n]], {n, 1, 10}]; Table[CoefficientList[p[x, n], x], {n, 1, 10}]; Flatten[%] b = Table[Apply[Plus, Re[CoefficientList[p[x, n], x]]], {n, 1, 10}]
CROSSREFS
Sequence in context: A345064 A076699 A373851 * A196308 A091862 A351564
KEYWORD
uned,sign
AUTHOR
STATUS
approved