A134885 Triangular sequence from polynomials that gives roots near 137.

1, 137, -1, -135, -137, 1, 134, 0, 137, -1, -133, 0, 0, -137, 1, 132, 0, 0, 0, 137, -1, -131, 0, 0, 0, 0, -137, 1, 130, 0, 0, 0, 0, 0, 137, -1

Offset

1,2

Comments

Alternative Mathematica code for larger polynomials: p[x_, n_] = (-1)^(n - 1)*(135 - n) + (-1)^(n - 1)*137*x^(n - 1) - (-1)^ n - 1)*x^n Table[p[x, n], {n, 2, 10}]

Links

Table of n, a(n) for n=1..36.

Formula

p(x,0)=1 p(x,1)=137-x p(x,n)=(-1)^(n-1)*(135-n)+(-1)^(n-1)*137*x^(n-1)-(-1)^(n-1)*x^n: n>2 a(m,n) = CoefficientList(p(x,n),x)

Example

p[x,134]
gives:
-1 - 137 x^133 + x^134
Triangular sequence:
{1},
{137, -1},
{-135, -137, 1},
{134, 0, 137, -1},
{-133, 0, 0, -137, 1},
{132, 0, 0, 0, 137, -1},
{-131, 0, 0, 0, 0, -137, 1},
{130, 0, 0, 0, 0, 0, 137, -1}

Mathematica

p[x_, n_] = (-1)^(n - 1)*(137 - n) + (-1)^(n - 1)*137*x^(n - 1) - (-1)^( n - 1)*x^n
a = Join[{1, 137 - x}, Table[p[x, n], {n, 2, 10}]]
c = Table[CoefficientList[a[[n]], x], {n, 1, Length[a]}]
Flatten[c]

Crossrefs

Sequence in context: A233254 A001330 A091510 * A259680 A082726 A189998

Adjacent sequences: A134882 A134883 A134884 * A134886 A134887 A134888

Keyword

uned,tabl,sign

Author

Roger L. Bagula, Jan 29 2008

Status

approved