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 A208540 Number of n-bead necklaces of 4 colors allowing reversal, with no adjacent beads having the same color. 2
 4, 6, 4, 21, 24, 92, 156, 498, 1096, 3210, 8052, 22913, 61320, 173088, 478316, 1351983, 3798240, 10781954, 30585828, 87230157, 249056136, 713387076, 2046590844, 5884491500, 16945772208, 48883660146, 141214768972 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 Marko Riedel et al., math.stackexchange, Proper colorings of necklaces Marko Riedel et al., math.stackexchange, Proper colorings of bracelets FORMULA a(2*n+1) = A106366(2*n+1)/2 for n > 0, a(2*n) = (A106366(2*n) + 2*3^n)/2. - Andrew Howroyd, Mar 12 2017 EXAMPLE All solutions for n=3 ..1....1....2....1 ..2....2....3....3 ..3....4....4....4 MATHEMATICA T[n_, k_] := If[n == 1, k, (DivisorSum[n, EulerPhi[n/#]*(k - 1)^# &]/n + If[OddQ[n], 1 - k, k*(k - 1)^(n/2)/2])/2]; a[n_] = T[n, 4]; Array[a, 27] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *) CROSSREFS Column 4 of A208544. Sequence in context: A185145 A258836 A292387 * A019195 A019089 A173462 Adjacent sequences:  A208537 A208538 A208539 * A208541 A208542 A208543 KEYWORD nonn AUTHOR R. H. Hardin, Feb 27 2012 STATUS approved

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Last modified May 23 18:08 EDT 2022. Contains 353993 sequences. (Running on oeis4.)