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 A051841 Number of binary Lyndon words with an even number of 1's. 15
 1, 0, 1, 1, 3, 4, 9, 14, 28, 48, 93, 165, 315, 576, 1091, 2032, 3855, 7252, 13797, 26163, 49929, 95232, 182361, 349350, 671088, 1290240, 2485504, 4792905, 9256395, 17894588, 34636833, 67106816, 130150493, 252641280, 490853403, 954429840, 1857283155, 3616800768, 7048151355, 13743869130, 26817356775 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Also number of trace 0 irreducible polynomials over GF(2). Also number of trace 0 Lyndon words over GF(2). REFERENCES May, Robert M. "Simple mathematical models with very complicated dynamics." Nature, Vol. 261, June 10, 1976, pp. 459-467; reprinted in The Theory of Chaotic Attractors, pp. 85-93. Springer, New York, NY, 2004. The sequences listed in Table 2 are A000079, A027375, A000031, A001037, A000048, A051841. - N. J. A. Sloane, Mar 17 2019 LINKS T. D. Noe, Table of n, a(n) for n = 1..300 FORMULA a(n) = ( Sum_{d|n} gcd(d, 2)*mu(d)*2^{n/d}) / (2n). a(n) ~ 2^(n-1) / n. - Vaclav Kotesovec, May 31 2019 EXAMPLE a(5) = 3 = |{ 00011, 00101, 01111 }|. MATHEMATICA a[n_] := Sum[GCD[d, 2]*MoebiusMu[d]*2^(n/d), {d, Divisors[n]}]/(2n); Table[a[n], {n, 1, 32}] (* Jean-François Alcover, May 14 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)%2==0, L(n, k), 0 ) ) / n; vector(33, n, a(n)) /* Joerg Arndt, Jun 28 2012 */ (Haskell) a051841 n = (sum \$ zipWith (\u v -> gcd 2 u * a008683 u * 2 ^ v)              ds \$ reverse ds) `div` (2 * n) where ds = a027750_row n -- Reinhard Zumkeller, Mar 17 2013 CROSSREFS Same as A001037 - A000048. Same as A042980 + A042979. Cf. A027750, A008683. Sequence in context: A002823 A109509 A006053 * A096081 A054162 A174783 Adjacent sequences:  A051838 A051839 A051840 * A051842 A051843 A051844 KEYWORD nonn,easy,nice AUTHOR Frank Ruskey, Dec 13 1999 STATUS approved

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Last modified August 10 16:56 EDT 2020. Contains 336381 sequences. (Running on oeis4.)