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A208716
Number of n-bead necklaces labeled with numbers 1..3 allowing reversal, with no adjacent beads differing by more than 1.
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
Stephan Mertens, Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph, arXiv:2408.08053 [math.CO], 2024. See p. 22.
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.
Sequence in context: A137700 A325267 A241544 * A195821 A372684 A208772
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 01 2012
STATUS
approved