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%I A087610
%S A087610 3,5,12,34,104,292,916,2791,8660,26538
%N A087610 Number of (-1,0,1) polynomials of degree-n irreducible over the integers.
%C A087610 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.
%H A087610 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               IrreduciblePolynomial.html">Irreducible Polynomial</a>
%e A087610 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.
%t A087610 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}]
%Y A087610 Cf. A087481 (irreducible polynomials of the form x^n +- x^(n-1) +- x^(n-2) 
               +- ... +- 1), A087482 (irreducible binary polynomials).
%Y A087610 Sequence in context: A066951 A046091 A002905 this_sequence A156436 A099791 
               A028268
%Y A087610 Adjacent sequences: A087607 A087608 A087609 this_sequence A087611 A087612 
               A087613
%K A087610 nonn
%O A087610 1,1
%A A087610 T. D. Noe (noe(AT)sspectra.com), Sep 11 2003

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