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 A208542 Number of n-bead necklaces of 6 colors allowing reversal, with no adjacent beads having the same color. 2
 6, 15, 20, 120, 312, 1505, 5580, 25395, 108520, 493131, 2219460, 10196680, 46950120, 218102685, 1017252828, 4768969770, 22439395680, 105966797755, 501933850740, 2384200683816, 11353265675240, 54186115056825, 259150629458220, 1241763804134805 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 FORMULA a(2n+1) = A106368(2n+1)/2 for n > 0, a(2n) = (A106368(2n) + 3*5^n)/2. - Andrew Howroyd, Mar 12 2017 EXAMPLE All solutions for n=3: ..3....2....1....2....2....3....3....1....1....1....1....2....1....2....1....1 ..4....4....2....5....3....5....4....5....3....3....4....3....3....3....4....2 ..6....5....5....6....6....6....5....6....5....4....5....4....6....5....6....3 .. ..2....1....1....4 ..4....2....2....5 ..6....4....6....6 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, 6]; Array[a, 24] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *) CROSSREFS Column 6 of A208544. Sequence in context: A196394 A162693 A056901 * A012412 A009092 A330205 Adjacent sequences:  A208539 A208540 A208541 * A208543 A208544 A208545 KEYWORD nonn AUTHOR R. H. Hardin, Feb 27 2012 EXTENSIONS a(19)-a(24) from Andrew Howroyd, Mar 12 2017 STATUS approved

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Last modified October 1 13:04 EDT 2020. Contains 337443 sequences. (Running on oeis4.)