A172972 Subtraction triangle based on A029826: c(n)=Product[A029826(i),{i,0,n)];t(n,m)=c(n)-c(m)-c(n-m).

-1, -1, -1, -1, -3, -1, -1, -1, -1, -1, -1, 0, 2, 0, -1, -1, -1, 2, 2, -1, -1, -1, -1, 1, 2, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 0, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 1, 1, -1, -1

Offset: 0

Author

Roger L. Bagula, Feb 06 2010

Keywords

• sign
• tabl
• uned

Comments

Row sums are:

{-1, -2, -5, -4, 0, 0, 0, 0, 0, 0, 0,...}.

Examples

			{-1},
{-1, -1},
{-1, -3, -1},
{-1, -1, -1, -1},
{-1, 0, 2, 0, -1},
{-1, -1, 2, 2, -1, -1},
{-1, -1, 1, 2, 1, -1, -1},
{-1, -1, 1, 1, 1, 1, -1, -1},
{-1, -1, 1, 1, 0, 1, 1, -1, -1},
{-1, -1, 1, 1, 0, 0, 1, 1, -1, -1},
{-1, -1, 1, 1, 0, 0, 0, 1, 1, -1, -1}
		

Crossrefs

A029826

Programs

Mathematica

(*A029826 Inverse of Salem polynomial : 1/(x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1).*)
p[x_] = (x^(10) + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1); q[ x_] = Expand[x^10*p[1/x]]; a = Table[SeriesCoefficient[Series[1/ q[x], {x, 0, 100}], n], {n, 0, 100}];
c[n_] := Product[a[[m]], {m, 1, n}];
t[n_, m_] := c[n] - (c[m] + c[n - m]);
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Formula

c(n)=Product[A029826(i),{i,0,n)];

t(n,m)=c(n)-c(m)-c(n-m)