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 A208538 Number of n-bead necklaces of n colors allowing reversal, with no adjacent beads having the same color. 2

%I

%S 1,1,1,21,102,1505,19995,365260,7456596,174489813,4545454545,

%T 130773238871,4115123283810,140620807064413,5185603185296625,

%U 205262771447683860,8680820740569200760,390641235316599920745,18637772246193096746253,939749336469457562916217

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

%H Andrew Howroyd, <a href="/A208538/b208538.txt">Table of n, a(n) for n = 1..80</a>

%F a(2n+1) = A208533(2n+1)/2 for n > 0, a(2n) = (A208533(2n) + n*(2n-1)^n)/2. - _Andrew Howroyd_, Mar 12 2017

%e All solutions for n=4:

%e ..1....1....1....1....2....1....1....1....2....1....1....3....2....2....1....1

%e ..2....4....3....2....3....2....3....3....4....3....2....4....3....4....2....2

%e ..4....2....2....3....2....4....1....4....2....2....1....3....2....3....1....1

%e ..2....4....4....2....3....3....3....3....4....3....3....4....4....4....2....4

%e ..

%e ..1....1....2....1....1

%e ..3....4....3....2....4

%e ..1....3....4....3....1

%e ..4....4....3....4....4

%t 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_ *)

%Y Diagonal of A208544.

%K nonn

%O 1,4

%A _R. H. Hardin_, Feb 27 2012

%E a(12)-a(20) from _Andrew Howroyd_, Mar 12 2017

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Last modified September 18 01:39 EDT 2021. Contains 347504 sequences. (Running on oeis4.)