A208671 - OEIS

%I #11 Mar 20 2017 09:50:40

%S 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,

%T 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,

%U 28,50,86,152,212,187,46,1,0,11,19,32,59,107,208,360,512,396,78,1,0,12,21,36

%N T(n,k) = number of 2n-bead necklaces labeled with numbers 1..k allowing reversal, with neighbors differing by exactly 1.

%C Table starts

%C .0.1..2...3...4...5....6....7....8....9...10..11..12..13.14.15.16

%C .0.1..3...5...7...9...11...13...15...17...19..21..23..25.27.29

%C .0.1..4...8..12..16...20...24...28...32...36..40..44..48.52

%C .0.1..6..14..23..32...41...50...59...68...77..86..95.104

%C .0.1..8..24..44..65...86..107..128..149..170.191.212

%C .0.1.13..47..97.152..208..264..320..376..432.488

%C .0.1.18..89.212.360..514..669..824..979.1134

%C .0.1.30.187.512.937.1398.1866.2335.2804

%H R. H. Hardin, <a href="/A208671/b208671.txt">Table of n, a(n) for n = 1..148</a>

%F T(n,k) = (2*A208727(n) + A220062(n+1,k))/4. - _Andrew Howroyd_, Mar 19 2017

%e All solutions for n=4, k=3:

%e ..1....1....1....1....1....2

%e ..2....2....2....2....2....3

%e ..3....1....1....1....3....2

%e ..2....2....2....2....2....3

%e ..1....3....1....1....3....2

%e ..2....2....2....2....2....3

%e ..3....3....3....1....3....2

%e ..2....2....2....2....2....3

%Y Column 3 is A000029.

%Y Cf. A208727, A220062.

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Feb 29 2012