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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.

%I A208671 #11 Mar 20 2017 09:50:40
%S A208671 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 A208671 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 A208671 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 A208671 T(n,k) = number of 2n-bead necklaces labeled with numbers 1..k allowing reversal, with neighbors differing by exactly 1.
%C A208671 Table starts
%C A208671 .0.1..2...3...4...5....6....7....8....9...10..11..12..13.14.15.16
%C A208671 .0.1..3...5...7...9...11...13...15...17...19..21..23..25.27.29
%C A208671 .0.1..4...8..12..16...20...24...28...32...36..40..44..48.52
%C A208671 .0.1..6..14..23..32...41...50...59...68...77..86..95.104
%C A208671 .0.1..8..24..44..65...86..107..128..149..170.191.212
%C A208671 .0.1.13..47..97.152..208..264..320..376..432.488
%C A208671 .0.1.18..89.212.360..514..669..824..979.1134
%C A208671 .0.1.30.187.512.937.1398.1866.2335.2804
%H A208671 R. H. Hardin, <a href="/A208671/b208671.txt">Table of n, a(n) for n = 1..148</a>
%F A208671 T(n,k) = (2*A208727(n) + A220062(n+1,k))/4. - _Andrew Howroyd_, Mar 19 2017
%e A208671 All solutions for n=4, k=3:
%e A208671 ..1....1....1....1....1....2
%e A208671 ..2....2....2....2....2....3
%e A208671 ..3....1....1....1....3....2
%e A208671 ..2....2....2....2....2....3
%e A208671 ..1....3....1....1....3....2
%e A208671 ..2....2....2....2....2....3
%e A208671 ..3....3....3....1....3....2
%e A208671 ..2....2....2....2....2....3
%Y A208671 Column 3 is A000029.
%Y A208671 Cf. A208727, A220062.
%K A208671 nonn,tabl
%O A208671 1,4
%A A208671 _R. H. Hardin_, Feb 29 2012