A208724 - OEIS

%I #13 Oct 31 2017 10:36:09

%S 4,7,12,25,52,131,316,835,2196,5935,16108,44369,122644,341803,956636,

%T 2690845,7596484,21524543,61171660,174342217,498112276,1426419859,

%U 4093181692,11767920119,33891544420,97764131647,282429537948,817028472961,2366564736724,6863038218843

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

%H Andrew Howroyd, <a href="/A208724/b208724.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = (1/n) * Sum_{d | n} totient(n/d) * A198635(d) / 2. - _Andrew Howroyd_, Mar 18 2017

%e All solutions for n=3:

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

%e ..5....2....4....3....2....3....4....2....3....4....2....3

%e ..4....1....3....2....3....4....3....3....2....5....1....4

%e ..5....2....4....3....2....3....4....4....3....4....2....5

%e ..4....3....3....2....3....4....5....3....4....5....1....4

%e ..5....2....4....3....2....3....4....2....3....4....2....3

%t a[n_] := (1/n)*DivisorSum[n, EulerPhi[n/#] * (2*3^# + 2) &] / 2;

%t Array[a, 30] (* _Jean-François Alcover_, Oct 31 2017, after _Andrew Howroyd_ *)

%Y Column 5 of A208727.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 01 2012

%E a(15)-a(30) from _Andrew Howroyd_, Mar 18 2017