|
Search: id:A087610
|
|
|
| A087610 |
|
Number of (-1,0,1) polynomials of degree-n irreducible over the integers. |
|
+0
7
|
| |
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
A (-1,0,1) polynomial is defined as a monic polynomial whose remaining coefficients are either -1, 0, or 1. For each n, there are 3^n polynomials to consider.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Irreducible Polynomial
|
|
EXAMPLE
|
a(2) = 5 because 1+x+x^2, 1+x^2, 1-x+x^2, -1+x+x^2, -1-x+x^2 are irreducible over the integers.
|
|
MATHEMATICA
|
Irreducible[p_, n_] := Module[{f}, f=FactorList[p, Modulus->n]; Length[f]==1 || Simplify[p-f[[2, 1]]]===0]; Table[xx=x^Range[0, n-1]; cnt=0; Do[p=x^n+xx.(IntegerDigits[i, 3, n]-1); If[Irreducible[p, 0], cnt++ ], {i, 0, 3^n-1}]; cnt, {n, 10}]
|
|
CROSSREFS
|
Cf. A087481 (irreducible polynomials of the form x^n +- x^(n-1) +- x^(n-2) +- ... +- 1), A087482 (irreducible binary polynomials).
Sequence in context: A066951 A046091 A002905 this_sequence A099791 A028268 A137162
Adjacent sequences: A087607 A087608 A087609 this_sequence A087611 A087612 A087613
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Sep 11 2003
|
|
|
Search completed in 0.002 seconds
|
