A208541 - OEIS

%I #14 Nov 01 2017 12:24:28

%S 5,10,10,55,102,430,1170,4435,14570,53764,190650,704370,2581110,

%T 9608050,35791470,134301715,505290270,1909209550,7233629130,

%U 27489127708,104715393910,399827748310,1529755308210,5864083338770,22517998136934,86607770318380

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

%H Andrew Howroyd, <a href="/A208541/b208541.txt">Table of n, a(n) for n = 1..100</a>

%F a(2n+1) = A106367(2n+1)/2 for n > 0, a(2n) = (A106367(2n) + 5*4^n/2)/2. - _Andrew Howroyd_, Mar 12 2017

%e All solutions for n=3:

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

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

%e ..4....3....4....4....5....5....5....5....5....5

%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, 5]; Array[a, 26] (* _Jean-François Alcover_, Nov 01 2017, after _Andrew Howroyd_ *)

%Y Column 5 of A208544.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 27 2012

%E a(21)-a(26) from _Andrew Howroyd_, Mar 12 2017