A208543 Number of n-bead necklaces of 7 colors allowing reversal, with no adjacent beads having the same color.

7, 21, 35, 231, 777, 4291, 19995, 107331, 559895, 3037314, 16490775, 90782986, 502334385, 2799220041, 15672833365, 88162676511, 497842924845, 2821127825971, 16035782631855, 91404068329560, 522308348593785, 2991403003191771, 17168048327252235, 98716281736491076

Offset

1,1

Links

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

Example

All solutions for n=3:
..1....1....5....2....1....3....1....4....1....3....3....1....1....2....3....2
..6....3....6....6....4....6....3....5....3....5....4....4....2....5....5....3
..7....6....7....7....7....7....4....6....7....7....5....6....4....6....6....4
..
..1....1....3....1....1....1....2....4....2....4....1....2....1....1....3....2
..2....2....4....2....2....4....4....6....5....5....5....4....5....3....4....3
..6....5....7....7....3....5....6....7....7....7....6....5....7....5....6....7
..
..2....2....2
..3....3....4
..6....5....7

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, 7]; Array[a, 24] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)

Crossrefs

Column 7 of A208544.

Sequence in context: A045849 A031008 A147587 * A009475 A063292 A045524

Adjacent sequences: A208540 A208541 A208542 * A208544 A208545 A208546

Keyword

nonn

Author

R. H. Hardin, Feb 27 2012

Extensions

a(18)-a(24) from Andrew Howroyd, Mar 12 2017

Status

approved