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

6, 15, 20, 120, 312, 1505, 5580, 25395, 108520, 493131, 2219460, 10196680, 46950120, 218102685, 1017252828, 4768969770, 22439395680, 105966797755, 501933850740, 2384200683816, 11353265675240, 54186115056825, 259150629458220, 1241763804134805

Offset: 1

Author

R. H. Hardin, Feb 27 2012

Keywords

• nonn

Examples

			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
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100

Crossrefs

Column 6 of A208544.

Programs

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 *)

Formula

a(2n+1) = A106368(2n+1)/2 for n > 0, a(2n) = (A106368(2n) + 3*5^n)/2. - Andrew Howroyd, Mar 12 2017

Extensions

a(19)-a(24) from Andrew Howroyd, Mar 12 2017