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%I #14 Mar 19 2017 01:12:34
%S 0,1,0,2,1,0,3,3,1,0,4,5,4,1,0,5,7,8,6,1,0,6,9,12,15,8,1,0,7,11,16,25,
%T 27,14,1,0,8,13,20,35,52,60,20,1,0,9,15,24,45,78,131,123,36,1,0,10,17,
%U 28,55,104,210,316,285,60,1,0,11,19,32,65,130,290,551,835,648,108,1,0,12,21,36
%N T(n,k)=Number of 2n-bead necklaces labeled with numbers 1..k not 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..15.16.17.18
%C .0.1..3...5...7....9...11...13...15...17...19...21...23..25..27..29.31.33
%C .0.1..4...8..12...16...20...24...28...32...36...40...44..48..52..56.60
%C .0.1..6..15..25...35...45...55...65...75...85...95..105.115.125.135
%C .0.1..8..27..52...78..104..130..156..182..208..234..260.286.312
%C .0.1.14..60.131..210..290..370..450..530..610..690..770.850
%C .0.1.20.123.316..551..796.1042.1288.1534.1780.2026.2272
%C .0.1.36.285.835.1569.2366.3175.3985.4795.5605.6415
%H R. H. Hardin, <a href="/A208727/b208727.txt">Table of n, a(n) for n = 1..183</a>
%e All solutions for n=5, k=3:
%e ..2....1....1....1....1....1....1....1
%e ..3....2....2....2....2....2....2....2
%e ..2....3....1....1....1....3....1....1
%e ..3....2....2....2....2....2....2....2
%e ..2....1....1....3....1....3....3....1
%e ..3....2....2....2....2....2....2....2
%e ..2....3....1....3....3....3....1....1
%e ..3....2....2....2....2....2....2....2
%e ..2....3....3....3....3....3....3....1
%e ..3....2....2....2....2....2....2....2
%Y Column 3 is A000031.
%Y Cf. A198632, A232441, A186740.
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Mar 01 2012