A131522 Expansions of p(x,n)=(x^n - 1)*(x^(n + 1) - 1) for n >= 1, triangle read by rows.

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

Offset

1,1

Links

Table of n, a(n) for n=1..118.

Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois Groups, Bull. London Math Soc. 28, (1996) pages 561-590 (dihedral group invariant on page 585).

Example

{1, -1, -1, 1},
{1, 0, -1, -1, 0, 1},
{1, 0,0, -1, -1, 0, 0, 1},
{1, 0, 0, 0, -1, -1, 0, 0, 0, 1},
{1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, -1, -1,0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0,0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}

Mathematica

p[n_] = ExpandAll[(x^n - 1)*(x^(n + 1) - 1)];
a = Table[CoefficientList[p[n], x], {n, 1, 10}];
Flatten[a]

Crossrefs

Sequence in context: A342892 A071036 A071038 * A221641 A144473 A011750

Adjacent sequences: A131519 A131520 A131521 * A131523 A131524 A131525

Keyword

tabf,easy,less,sign

Author

Roger L. Bagula, Aug 24 2007

Status

approved