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A208671
T(n,k) = number of 2n-bead necklaces labeled with numbers 1..k allowing reversal, with neighbors differing by exactly 1.
7
0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 5, 4, 1, 0, 5, 7, 8, 6, 1, 0, 6, 9, 12, 14, 8, 1, 0, 7, 11, 16, 23, 24, 13, 1, 0, 8, 13, 20, 32, 44, 47, 18, 1, 0, 9, 15, 24, 41, 65, 97, 89, 30, 1, 0, 10, 17, 28, 50, 86, 152, 212, 187, 46, 1, 0, 11, 19, 32, 59, 107, 208, 360, 512, 396, 78, 1, 0, 12, 21, 36
OFFSET
1,4
COMMENTS
Table starts
.0.1..2...3...4...5....6....7....8....9...10..11..12..13.14.15.16
.0.1..3...5...7...9...11...13...15...17...19..21..23..25.27.29
.0.1..4...8..12..16...20...24...28...32...36..40..44..48.52
.0.1..6..14..23..32...41...50...59...68...77..86..95.104
.0.1..8..24..44..65...86..107..128..149..170.191.212
.0.1.13..47..97.152..208..264..320..376..432.488
.0.1.18..89.212.360..514..669..824..979.1134
.0.1.30.187.512.937.1398.1866.2335.2804
LINKS
FORMULA
T(n,k) = (2*A208727(n) + A220062(n+1,k))/4. - Andrew Howroyd, Mar 19 2017
EXAMPLE
All solutions for n=4, k=3:
..1....1....1....1....1....2
..2....2....2....2....2....3
..3....1....1....1....3....2
..2....2....2....2....2....3
..1....3....1....1....3....2
..2....2....2....2....2....3
..3....3....3....1....3....2
..2....2....2....2....2....3
CROSSREFS
Column 3 is A000029.
Sequence in context: A122202 A122285 A100224 * A208727 A242378 A268820
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 29 2012
STATUS
approved