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A208671 T(n,k) = number of 2n-bead necklaces labeled with numbers 1..k allowing reversal, with neighbors differing by exactly 1. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 11 21:28 EST 2019. Contains 329937 sequences. (Running on oeis4.)