%I #13 Nov 01 2017 12:24:41
%S 7,21,35,231,777,4291,19995,107331,559895,3037314,16490775,90782986,
%T 502334385,2799220041,15672833365,88162676511,497842924845,
%U 2821127825971,16035782631855,91404068329560,522308348593785,2991403003191771,17168048327252235,98716281736491076
%N Number of n-bead necklaces of 7 colors allowing reversal, with no adjacent beads having the same color.
%H Andrew Howroyd, <a href="/A208543/b208543.txt">Table of n, a(n) for n = 1..100</a>
%e All solutions for n=3:
%e ..1....1....5....2....1....3....1....4....1....3....3....1....1....2....3....2
%e ..6....3....6....6....4....6....3....5....3....5....4....4....2....5....5....3
%e ..7....6....7....7....7....7....4....6....7....7....5....6....4....6....6....4
%e ..
%e ..1....1....3....1....1....1....2....4....2....4....1....2....1....1....3....2
%e ..2....2....4....2....2....4....4....6....5....5....5....4....5....3....4....3
%e ..6....5....7....7....3....5....6....7....7....7....6....5....7....5....6....7
%e ..
%e ..2....2....2
%e ..3....3....4
%e ..6....5....7
%t 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, 7]; Array[a, 24] (* _Jean-François Alcover_, Nov 01 2017, after _Andrew Howroyd_ *)
%Y Column 7 of A208544.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 27 2012
%E a(18)-a(24) from _Andrew Howroyd_, Mar 12 2017