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

1,1

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: A162693 A343893 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