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

0,5

Comments

Row sums are:

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

Links

Table of n, a(n) for n=0..65.

Formula

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

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

Example

{-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}

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[%]

Crossrefs

A029826

Sequence in context: A134108 A176851 A205535 * A175739 A371149 A260196

Adjacent sequences: A172969 A172970 A172971 * A172973 A172974 A172975

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Feb 06 2010

Status

approved