A208541 Number of n-bead necklaces of 5 colors allowing reversal, with no adjacent beads having the same color.

5, 10, 10, 55, 102, 430, 1170, 4435, 14570, 53764, 190650, 704370, 2581110, 9608050, 35791470, 134301715, 505290270, 1909209550, 7233629130, 27489127708, 104715393910, 399827748310, 1529755308210, 5864083338770, 22517998136934, 86607770318380

Offset

1,1

Links

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

Formula

a(2n+1) = A106367(2n+1)/2 for n > 0, a(2n) = (A106367(2n) + 5*4^n/2)/2. - Andrew Howroyd, Mar 12 2017

Example

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

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, 5]; Array[a, 26] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)

Crossrefs

Column 5 of A208544.

Sequence in context: A242894 A256641 A032242 * A324593 A107975 A262665

Adjacent sequences: A208538 A208539 A208540 * A208542 A208543 A208544

Keyword

nonn

Author

R. H. Hardin, Feb 27 2012

Extensions

a(21)-a(26) from Andrew Howroyd, Mar 12 2017

Status

approved