A208538 Number of n-bead necklaces of n colors allowing reversal, with no adjacent beads having the same color.

1, 1, 1, 21, 102, 1505, 19995, 365260, 7456596, 174489813, 4545454545, 130773238871, 4115123283810, 140620807064413, 5185603185296625, 205262771447683860, 8680820740569200760, 390641235316599920745, 18637772246193096746253, 939749336469457562916217

Offset: 1

Author

R. H. Hardin, Feb 27 2012

Keywords

• nonn

Examples

			All solutions for n=4:
..1....1....1....1....2....1....1....1....2....1....1....3....2....2....1....1
..2....4....3....2....3....2....3....3....4....3....2....4....3....4....2....2
..4....2....2....3....2....4....1....4....2....2....1....3....2....3....1....1
..2....4....4....2....3....3....3....3....4....3....3....4....4....4....2....4
..
..1....1....2....1....1
..3....4....3....2....4
..1....3....4....3....1
..4....4....3....4....4
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..80

Crossrefs

Diagonal 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, n]; Array[a, 20] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)

Formula

a(2n+1) = A208533(2n+1)/2 for n > 0, a(2n) = (A208533(2n) + n*(2n-1)^n)/2. - Andrew Howroyd, Mar 12 2017

Extensions

a(12)-a(20) from Andrew Howroyd, Mar 12 2017