A208671 T(n,k) = number of 2n-bead necklaces labeled with numbers 1..k allowing reversal, with neighbors differing by exactly 1.

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

Author

R. H. Hardin, Feb 29 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..148

Crossrefs

Column 3 is A000029.

Cf. A208727, A220062.

Formula

T(n,k) = (2*A208727(n) + A220062(n+1,k))/4. - Andrew Howroyd, Mar 19 2017