A134885 - OEIS

%I #3 Mar 30 2012 17:34:22

%S 1,137,-1,-135,-137,1,134,0,137,-1,-133,0,0,-137,1,132,0,0,0,137,-1,

%T -131,0,0,0,0,-137,1,130,0,0,0,0,0,137,-1

%N Triangular sequence from polynomials that gives roots near 137.

%C 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}]

%F 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)

%e p[x,134]

%e gives:

%e -1 - 137 x^133 + x^134

%e Triangular sequence:

%e {1},

%e {137, -1},

%e {-135, -137, 1},

%e {134, 0, 137, -1},

%e {-133, 0, 0, -137, 1},

%e {132, 0, 0, 0, 137, -1},

%e {-131, 0, 0, 0, 0, -137, 1},

%e {130, 0, 0, 0, 0, 0, 137, -1}

%t p[x_, n_] = (-1)^(n - 1)*(137 - n) + (-1)^(n - 1)*137*x^(n - 1) - (-1)^( n - 1)*x^n

%t a = Join[{1, 137 - x}, Table[p[x, n], {n, 2, 10}]]

%t c = Table[CoefficientList[a[[n]], x], {n, 1, Length[a]}]

%t Flatten[c]

%K uned,tabl,sign

%O 1,2

%A _Roger L. Bagula_, Jan 29 2008