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

1,1

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Column 5 of A208727.

Sequence in context: A322619 A299900 A215329 * A183336 A102953 A111157

Adjacent sequences: A208721 A208722 A208723 * A208725 A208726 A208727

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Extensions

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

Status

approved