A208716 Number of n-bead necklaces labeled with numbers 1..3 allowing reversal, with no adjacent beads differing by more than 1.

3, 5, 7, 12, 18, 34, 56, 111, 207, 427, 859, 1851, 3930, 8672, 19092, 42845, 96243, 218567, 497183, 1138084, 2610226, 6009662, 13861968, 32057868, 74260243, 172351415, 400589343, 932486879, 2173368730, 5071877864, 11849063220, 27711739481

Offset

1,1

Links

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

Formula

a(2n+1) = (1/2) * (A208772(2n+1) + A078057(n+1)). - Andrew Howroyd, Mar 03 2017

a(2n) = (1/2) * A208772(2n) + (1/4) * (A078057(n) + A078057(n+1)). - Andrew Howroyd, Mar 03 2017

Example

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

Crossrefs

Column 3 of A208721.

Cf. A208772, A078057.

Sequence in context: A137700 A325267 A241544 * A195821 A208772 A071810

Adjacent sequences: A208713 A208714 A208715 * A208717 A208718 A208719

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Status

approved