A208723 Number of 2n-bead necklaces labeled with numbers 1..4 not allowing reversal, with neighbors differing by exactly 1.

3, 5, 8, 15, 27, 60, 123, 285, 648, 1529, 3603, 8680, 20883, 50825, 124056, 304575, 750123, 1855100, 4600203, 11442087, 28527448, 71292605, 178526883, 447919420, 1125750147, 2833906685, 7144450568, 18036423975, 45591631803, 115381823348

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) * A005248(d). - Andrew Howroyd, Mar 18 2017

Example

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

Crossrefs

Column 4 of A208727.

Sequence in context: A052977 A191633 A215327 * A285010 A352917 A099846

Adjacent sequences: A208720 A208721 A208722 * A208724 A208725 A208726

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Extensions

a(26)-a(30) from Andrew Howroyd, Mar 18 2017

Status

approved