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 A042982 Number of degree-n irreducible polynomials over GF(2) with trace = 1 and subtrace = 1. 7
 0, 1, 0, 1, 2, 2, 5, 8, 13, 27, 45, 85, 160, 288, 550, 1024, 1920, 3654, 6885, 13107, 24989, 47616, 91225, 174760, 335462, 645435, 1242600, 2396745, 4628480, 8947294, 17318945, 33554432, 65074253, 126324495, 245424829, 477218560, 928645120, 1808400384, 3524082400, 6871947672, 13408665600, 26178873147 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 K. Cattell, C. R. Miers, F. Ruskey, J. Sawada and M. Serra, The Number of Irreducible Polynomials over GF(2) with Given Trace and Subtrace, J. Comb. Math. and Comb. Comp., 47 (2003) 31-64. FORMULA a(n) = (1/n) * Sum_{ L(n, k) : n+k = 3 mod 4}, where L(n, k) = Sum_{ mu(d)*binomial(n/d, k/d) : d|gcd(n, k)}. MATHEMATICA 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] == 3, L[n, k], 0], {k, 0, n}]; Table[a[n], {n, 1, 32}] (* Jean-François Alcover, Jun 28 2012, from formula *) PROG (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==3, L(n, k), 0 ) ) / n; vector(33, n, a(n)) /* Joerg Arndt, Jun 28 2012 */ CROSSREFS Cf. A042979, A042980, A042981. Cf. A074027, A074028, A074029, A074030. Sequence in context: A293674 A052527 A335443 * A340249 A006367 A246807 Adjacent sequences: A042979 A042980 A042981 * A042983 A042984 A042985 KEYWORD nonn AUTHOR STATUS approved

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Last modified February 5 18:15 EST 2023. Contains 360087 sequences. (Running on oeis4.)