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 A087610 Number of (-1,0,1) polynomials of degree-n irreducible over the integers. 6
 3, 5, 12, 34, 104, 292, 916, 2791, 8660, 26538, 81584, 248554 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. MAPLE F:= proc(n) local T, count, t, x, p;       if n::odd then         T:= combinat:-cartprod([[-1, 0, 1]\$(n-1), [1]])       else         T:= combinat:-cartprod([[-1, 0, 1]\$(n-1), [-1, 1]])       fi;       count:= 0;       while not T[finished] do          t:= T[nextvalue]();          p:= x^n + add(t[i]*x^(n-i), i=1..n);          if irreduc(p) then count:= count+1 fi;       od;       if n::odd then 2*count else count fi; end proc: 3, seq(F(n), n=2..11); # Robert Israel, Dec 10 2015 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: A002905 A220832 A323270 * A243013 A191636 A267337 Adjacent sequences:  A087607 A087608 A087609 * A087611 A087612 A087613 KEYWORD nonn,more AUTHOR T. D. Noe, Sep 11 2003 EXTENSIONS a(11) and a(12) from Robert Israel, Dec 10 2015 STATUS approved

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Last modified June 24 14:20 EDT 2021. Contains 345417 sequences. (Running on oeis4.)