A208727 T(n,k)=Number of 2n-bead necklaces labeled with numbers 1..k not 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, 15, 8, 1, 0, 7, 11, 16, 25, 27, 14, 1, 0, 8, 13, 20, 35, 52, 60, 20, 1, 0, 9, 15, 24, 45, 78, 131, 123, 36, 1, 0, 10, 17, 28, 55, 104, 210, 316, 285, 60, 1, 0, 11, 19, 32, 65, 130, 290, 551, 835, 648, 108, 1, 0, 12, 21, 36

Offset: 1

Author

R. H. Hardin, Mar 01 2012

Keywords

• nonn
• tabl

Comments

Table starts

.0.1..2...3...4....5....6....7....8....9...10...11...12..13..14..15.16.17.18

.0.1..3...5...7....9...11...13...15...17...19...21...23..25..27..29.31.33

.0.1..4...8..12...16...20...24...28...32...36...40...44..48..52..56.60

.0.1..6..15..25...35...45...55...65...75...85...95..105.115.125.135

.0.1..8..27..52...78..104..130..156..182..208..234..260.286.312

.0.1.14..60.131..210..290..370..450..530..610..690..770.850

.0.1.20.123.316..551..796.1042.1288.1534.1780.2026.2272

.0.1.36.285.835.1569.2366.3175.3985.4795.5605.6415

Examples

			All solutions for n=5, k=3:
..2....1....1....1....1....1....1....1
..3....2....2....2....2....2....2....2
..2....3....1....1....1....3....1....1
..3....2....2....2....2....2....2....2
..2....1....1....3....1....3....3....1
..3....2....2....2....2....2....2....2
..2....3....1....3....3....3....1....1
..3....2....2....2....2....2....2....2
..2....3....3....3....3....3....3....1
..3....2....2....2....2....2....2....2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..183

Crossrefs

Column 3 is A000031.

Cf. A198632, A232441, A186740.