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

1,4

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

Links

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

Example

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

Crossrefs

Column 3 is A000031.

Cf. A198632, A232441, A186740.

Sequence in context: A122285 A100224 A208671 * A242378 A268820 A199011

Adjacent sequences: A208724 A208725 A208726 * A208728 A208729 A208730

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 01 2012

Status

approved