A208721 T(n,k) = number of n-bead necklaces labeled with numbers 1..k allowing reversal, with no adjacent beads differing by more than 1.

1, 2, 1, 3, 3, 1, 4, 5, 4, 1, 5, 7, 7, 6, 1, 6, 9, 10, 12, 8, 1, 7, 11, 13, 18, 18, 13, 1, 8, 13, 16, 24, 28, 34, 18, 1, 9, 15, 19, 30, 38, 56, 56, 30, 1, 10, 17, 22, 36, 48, 78, 98, 111, 46, 1, 11, 19, 25, 42, 58, 100, 140, 208, 207, 78, 1, 12, 21, 28, 48, 68, 122, 182, 306, 418, 427, 126

Offset

1,2

Comments

Table starts

.1..2...3...4...5...6...7...8...9..10..11..12...13...14...15...16...17...18

.1..3...5...7...9..11..13..15..17..19..21..23...25...27...29...31...33...35

.1..4...7..10..13..16..19..22..25..28..31..34...37...40...43...46...49...52

.1..6..12..18..24..30..36..42..48..54..60..66...72...78...84...90...96..102

.1..8..18..28..38..48..58..68..78..88..98.108..118..128..138..148..158..168

.1.13..34..56..78.100.122.144.166.188.210.232..254..276..298..320..342..364

.1.18..56..98.140.182.224.266.308.350.392.434..476..518..560..602..644..686

.1.30.111.208.306.404.502.600.698.796.894.992.1090.1188.1286.1384.1482.1580

Links

R. H. Hardin, Table of n, a(n) for n = 1..397

Example

All solutions for n=4, k=3:
..2....3....2....2....1....2....1....2....1....1....1....1
..3....3....2....3....1....2....1....2....2....2....1....2
..2....3....3....3....2....2....1....2....1....3....1....2
..3....3....3....3....2....2....1....3....2....2....2....2

Crossrefs

Column 2 is A000029.

Sequence in context: A286312 A278492 A128139 * A208777 A104732 A132108

Adjacent sequences: A208718 A208719 A208720 * A208722 A208723 A208724

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 01 2012

Status

approved