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A208724 Number of 2n-bead necklaces labeled with numbers 1..5 not allowing reversal, with neighbors differing by exactly 1.

%I A208724 #13 Oct 31 2017 10:36:09
%S A208724 4,7,12,25,52,131,316,835,2196,5935,16108,44369,122644,341803,956636,
%T A208724 2690845,7596484,21524543,61171660,174342217,498112276,1426419859,
%U A208724 4093181692,11767920119,33891544420,97764131647,282429537948,817028472961,2366564736724,6863038218843
%N A208724 Number of 2n-bead necklaces labeled with numbers 1..5 not allowing reversal, with neighbors differing by exactly 1.
%H A208724 Andrew Howroyd, <a href="/A208724/b208724.txt">Table of n, a(n) for n = 1..100</a>
%F A208724 a(n) = (1/n) * Sum_{d | n} totient(n/d) * A198635(d) / 2. - _Andrew Howroyd_, Mar 18 2017
%e A208724 All solutions for n=3:
%e A208724 ..4....1....3....2....1....2....3....1....2....3....1....2
%e A208724 ..5....2....4....3....2....3....4....2....3....4....2....3
%e A208724 ..4....1....3....2....3....4....3....3....2....5....1....4
%e A208724 ..5....2....4....3....2....3....4....4....3....4....2....5
%e A208724 ..4....3....3....2....3....4....5....3....4....5....1....4
%e A208724 ..5....2....4....3....2....3....4....2....3....4....2....3
%t A208724 a[n_] := (1/n)*DivisorSum[n, EulerPhi[n/#] * (2*3^# + 2) &] / 2;
%t A208724 Array[a, 30] (* _Jean-François Alcover_, Oct 31 2017, after _Andrew Howroyd_ *)
%Y A208724 Column 5 of A208727.
%K A208724 nonn
%O A208724 1,1
%A A208724 _R. H. Hardin_, Mar 01 2012
%E A208724 a(15)-a(30) from _Andrew Howroyd_, Mar 18 2017