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.

-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}.

Links

Table of n, a(n) for n=1..91.

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: A076699 A378442 A373851 * A196308 A091862 A351564

Adjacent sequences: A142717 A142718 A142719 * A142721 A142722 A142723

Keyword

uned,sign

Author

Roger L. Bagula and Gary W. Adamson, Sep 27 2008

Status

approved