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A208541 Number of n-bead necklaces of 5 colors allowing reversal, with no adjacent beads having the same color. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Nov 01 2017, after Andrew Howroyd *)

CROSSREFS

Column 5 of A208544.

Sequence in context: A242894 A256641 A032242 * A107975 A262665 A106792

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

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Last modified November 22 15:27 EST 2017. Contains 295089 sequences.