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 A045687 Number of 2n-bead balanced binary necklaces of fundamental period 2n which are equivalent to their reversed complement, but are not equivalent to their reverse and complement. 3
 0, 0, 0, 2, 4, 12, 24, 56, 112, 238, 480, 992, 1980, 4032, 8064, 16242, 32512, 65280, 130536, 261632, 523260, 1047494, 2095104, 4192256, 8384400, 16773108, 33546240, 67100432, 134201340, 268419072, 536837640, 1073709056, 2147418112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The number of length 2n balanced binary Lyndon words which are equivalent to their reversed complement is A000740(n) and the number which are equivalent to their reverse, complement and reversed complement is A045683(n). - Andrew Howroyd, Sep 28 2017 LINKS Joerg Arndt, Matters Computational (The Fxtbook), p.119 FORMULA From Andrew Howroyd, Sep 28 2017: (Start) Moebius transform of A045678. a(n) = A000740(n) - A045683(n). (End) MATHEMATICA a740[n_] := DivisorSum[n, MoebiusMu[n/#]*2^(#-1)&]; a45674[0] = 1; a45674[n_] := Module[{t = 0, r = n}, While[EvenQ[r], r = Quotient[r, 2]; t += 2^(r-1)]; t + 2^Quotient[r, 2]]; a45683[0] = 1; a45683[n_] := DivisorSum[n, MoebiusMu[n/#]*a45674[#]&]; a[0] = 0; a[n_] := a740[n] - a45683[n]; Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Sep 30 2017, after Andrew Howroyd *) CROSSREFS Cf. A000740, A045669, A045678, A045683. Sequence in context: A133411 A201078 A004645 * A233411 A057422 A036045 Adjacent sequences:  A045684 A045685 A045686 * A045688 A045689 A045690 KEYWORD nonn AUTHOR EXTENSIONS Incorrect formulas and comments removed by Andrew Howroyd, Sep 28 2017 STATUS approved

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Last modified June 4 05:19 EDT 2020. Contains 334815 sequences. (Running on oeis4.)