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A208542 Number of n-bead necklaces of 6 colors allowing reversal, with no adjacent beads having the same color.

%I A208542 #16 Nov 01 2017 12:24:34
%S A208542 6,15,20,120,312,1505,5580,25395,108520,493131,2219460,10196680,
%T A208542 46950120,218102685,1017252828,4768969770,22439395680,105966797755,
%U A208542 501933850740,2384200683816,11353265675240,54186115056825,259150629458220,1241763804134805
%N A208542 Number of n-bead necklaces of 6 colors allowing reversal, with no adjacent beads having the same color.
%H A208542 Andrew Howroyd, <a href="/A208542/b208542.txt">Table of n, a(n) for n = 1..100</a>
%F A208542 a(2n+1) = A106368(2n+1)/2 for n > 0, a(2n) = (A106368(2n) + 3*5^n)/2. - _Andrew Howroyd_, Mar 12 2017
%e A208542 All solutions for n=3:
%e A208542 ..3....2....1....2....2....3....3....1....1....1....1....2....1....2....1....1
%e A208542 ..4....4....2....5....3....5....4....5....3....3....4....3....3....3....4....2
%e A208542 ..6....5....5....6....6....6....5....6....5....4....5....4....6....5....6....3
%e A208542 ..
%e A208542 ..2....1....1....4
%e A208542 ..4....2....2....5
%e A208542 ..6....4....6....6
%t A208542 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_ *)
%Y A208542 Column 6 of A208544.
%K A208542 nonn
%O A208542 1,1
%A A208542 _R. H. Hardin_, Feb 27 2012
%E A208542 a(19)-a(24) from _Andrew Howroyd_, Mar 12 2017