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A042979
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Number of degree-n irreducible polynomials over GF(2) with trace = 0 and subtrace = 1.
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11
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0, 0, 1, 0, 2, 2, 4, 8, 13, 24, 48, 80, 160, 288, 541, 1024, 1920, 3626, 6912, 13056, 24989, 47616, 91136, 174760, 335462, 645120, 1242904, 2396160, 4628480, 8947294, 17317888, 33554432, 65074253, 126320640, 245428574, 477211280, 928645120, 1808400384, 3524068955, 6871947672, 13408665600, 26178823218
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OFFSET
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1,5
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LINKS
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FORMULA
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a(n) = (1/n) * Sum_{k=0..n, n+k == 0 (mod 4)} L(n, k), where L(n, k) = Sum_{d|gcd(n, k)} mu(d)*binomial(n/d, k/d).
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MATHEMATICA
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L[n_, k_] := Sum[ MoebiusMu[d]*Binomial[n/d, k/d], {d, Divisors[GCD[n, k]]}]/n; a[n_] := Sum[ If[ Mod[n+k, 4] == 0, L[n, k], 0], {k, 0, n}]; Table[a[n], {n, 1, 32}] (* Jean-François Alcover, Jun 28 2012, from formula *)
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PROG
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(PARI)
L(n, k) = sumdiv(gcd(n, k), d, moebius(d) * binomial(n/d, k/d) );
a(n) = sum(k=0, n, if( (n+k)%4==0, L(n, k), 0 ) ) / n;
vector(33, n, a(n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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