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 A059078 Number of orientable necklaces with 2n beads and two colors which when turned over produce their own color complement. 1
 0, 0, 0, 1, 2, 6, 12, 27, 54, 113, 228, 465, 934, 1890, 3798, 7644, 15350, 30840, 61878, 124173, 249008, 499318, 1000866, 2005971, 4019446, 8053062, 16131780, 32311665, 64711820, 129589530, 259487040, 519552495, 1040186358, 2082408354 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Clearly in each necklace the number of beads of each of the two colors must be equal and so the number of beads must be even, if a(n) is to be positive. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA a(n) = A059076(2*n) - 2*A059053(2*n). a(n) = A000029(2*n) - A000013(2*n) - A000079(n-1). MATHEMATICA a13[n_] := DivisorSum[n, EulerPhi@(2*#)*2^(n/#)&]/(2*n); a29[n_] := (1/4)*(Mod[n, 2] + 3)*2^Quotient[n, 2] + DivisorSum[n, EulerPhi[#]*2^(n/#)&]/(2*n); a[0] = 0; a[n_] := a29[2*n] - a13[2*n] - 2^(n - 1); Array[a, 34, 0] (* Jean-François Alcover, Nov 05 2017 *) CROSSREFS Sequence in context: A289443 A029863 A091919 * A166963 A188476 A155583 Adjacent sequences:  A059075 A059076 A059077 * A059079 A059080 A059081 KEYWORD nonn AUTHOR Henry Bottomley, Dec 22 2000 EXTENSIONS More terms from Vladeta Jovovic, Mar 06 2001 STATUS approved

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)