A140885 Triangle T(n,k) read by rows: the coefficient [x^k] ( Phi(n,x)+x^n*Phi(n,1/x)) related to cyclotomic polynomials Phi(n,x).

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

Offset

0,5

Comments

Row sums are: 0, 0, 4, 6, 4, 10, 2, 14, 4, 6, 2, 22, 2, 26, 2, 2, 4, 34, 2, 38, 2,...

Links

Table of n, a(n) for n=0..107.

Formula

T(n,k) = T(n,n-k) .

Example

0; # x+x^0*(1/x) = x+1/x
0, 0; # x-1+x*(1/x-1) = 0
1, 2, 1; # x+1+x^2*(1/x+1) = 1+2*x+x^2
1, 2, 2, 1;
1, 0, 2, 0, 1;
1, 2, 2, 2, 2, 1;
1, -1, 1, 0, 1, -1, 1;
1, 2, 2, 2, 2, 2, 2, 1;
1, 0, 0, 0, 2, 0, 0, 0, 1;
1, 0, 0, 2, 0, 0, 2, 0, 0, 1;
1, -1, 1, -1, 1, 0, 1, -1, 1, -1, 1;

Mathematica

Clear[p, x, n, m, a]; p[x_, n_] := Cyclotomic[n, x] + ExpandAll[x^n*Cyclotomic[n, 1/x]]; Table[p[x, n], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]

Crossrefs

Cf. A013595.

Sequence in context: A190672 A327910 A242998 * A064286 A002471 A218622

Adjacent sequences: A140882 A140883 A140884 * A140886 A140887 A140888

Keyword

tabl,sign

Author

Roger L. Bagula and Gary W. Adamson, Jul 22 2008

Extensions

All entries replaced to comply with the definition and examples - The Assoc. Eds. of the OEIS, Oct 12 2010

Status

approved