A172972 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

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