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

Author

R. H. Hardin, Mar 01 2012

Keywords

• nonn

Examples

			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
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100
• Stephan Mertens, Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph, arXiv:2408.08053 [math.CO], 2024. See p. 22.

Crossrefs

Column 3 of A208721.

Cf. A208772, A078057.

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