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

4, 7, 12, 25, 52, 131, 316, 835, 2196, 5935, 16108, 44369, 122644, 341803, 956636, 2690845, 7596484, 21524543, 61171660, 174342217, 498112276, 1426419859, 4093181692, 11767920119, 33891544420, 97764131647, 282429537948, 817028472961, 2366564736724, 6863038218843

Offset: 1

Author

R. H. Hardin, Mar 01 2012

Keywords

• nonn

Examples

			All solutions for n=3:
..4....1....3....2....1....2....3....1....2....3....1....2
..5....2....4....3....2....3....4....2....3....4....2....3
..4....1....3....2....3....4....3....3....2....5....1....4
..5....2....4....3....2....3....4....4....3....4....2....5
..4....3....3....2....3....4....5....3....4....5....1....4
..5....2....4....3....2....3....4....2....3....4....2....3
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100

Crossrefs

Column 5 of A208727.

Programs

Mathematica

a[n_] := (1/n)*DivisorSum[n, EulerPhi[n/#] * (2*3^# + 2) &] / 2;
Array[a, 30] (* Jean-François Alcover, Oct 31 2017, after Andrew Howroyd *)

Formula

a(n) = (1/n) * Sum_{d | n} totient(n/d) * A198635(d) / 2. - Andrew Howroyd, Mar 18 2017

Extensions

a(15)-a(30) from Andrew Howroyd, Mar 18 2017