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A208721 T(n,k) = number of n-bead necklaces labeled with numbers 1..k allowing reversal, with no adjacent beads differing by more than 1.

%I A208721 #7 Mar 13 2017 00:28:55
%S A208721 1,2,1,3,3,1,4,5,4,1,5,7,7,6,1,6,9,10,12,8,1,7,11,13,18,18,13,1,8,13,
%T A208721 16,24,28,34,18,1,9,15,19,30,38,56,56,30,1,10,17,22,36,48,78,98,111,
%U A208721 46,1,11,19,25,42,58,100,140,208,207,78,1,12,21,28,48,68,122,182,306,418,427,126
%N A208721 T(n,k) = number of n-bead necklaces labeled with numbers 1..k allowing reversal, with no adjacent beads differing by more than 1.
%C A208721 Table starts
%C A208721 .1..2...3...4...5...6...7...8...9..10..11..12...13...14...15...16...17...18
%C A208721 .1..3...5...7...9..11..13..15..17..19..21..23...25...27...29...31...33...35
%C A208721 .1..4...7..10..13..16..19..22..25..28..31..34...37...40...43...46...49...52
%C A208721 .1..6..12..18..24..30..36..42..48..54..60..66...72...78...84...90...96..102
%C A208721 .1..8..18..28..38..48..58..68..78..88..98.108..118..128..138..148..158..168
%C A208721 .1.13..34..56..78.100.122.144.166.188.210.232..254..276..298..320..342..364
%C A208721 .1.18..56..98.140.182.224.266.308.350.392.434..476..518..560..602..644..686
%C A208721 .1.30.111.208.306.404.502.600.698.796.894.992.1090.1188.1286.1384.1482.1580
%H A208721 R. H. Hardin, <a href="/A208721/b208721.txt">Table of n, a(n) for n = 1..397</a>
%e A208721 All solutions for n=4, k=3:
%e A208721 ..2....3....2....2....1....2....1....2....1....1....1....1
%e A208721 ..3....3....2....3....1....2....1....2....2....2....1....2
%e A208721 ..2....3....3....3....2....2....1....2....1....3....1....2
%e A208721 ..3....3....3....3....2....2....1....3....2....2....2....2
%Y A208721 Column 2 is A000029.
%K A208721 nonn,tabl
%O A208721 1,2
%A A208721 _R. H. Hardin_, Mar 01 2012