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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
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 * A335712 A356465 A166963
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 June 23 03:01 EDT 2024. Contains 373629 sequences. (Running on oeis4.)