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

1,4

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

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

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.

Cf. A208727, A220062.

Sequence in context: A122202 A122285 A100224 * A208727 A242378 A268820

Adjacent sequences: A208668 A208669 A208670 * A208672 A208673 A208674

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 29 2012

Status

approved