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 A209115 T(n,k)=Number of n-bead necklaces labelled with numbers -k..k not allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2 13
 1, 1, 2, 1, 3, 1, 1, 4, 5, 5, 1, 5, 11, 22, 5, 1, 6, 19, 55, 63, 15, 1, 7, 29, 120, 261, 238, 25, 1, 8, 41, 221, 741, 1373, 865, 68, 1, 9, 55, 362, 1683, 5032, 7377, 3417, 139, 1, 10, 71, 559, 3325, 14037, 35253, 41256, 13607, 354, 1, 11, 89, 816, 5935, 32802, 121117, 255821 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Table starts ..1....1.....1......1.......1.......1.......1........1........1.........1 ..2....3.....4......5.......6.......7.......8........9.......10........11 ..1....5....11.....19......29......41......55.......71.......89.......109 ..5...22....55....120.....221.....362.....559......816.....1137......1538 ..5...63...261....741....1683....3325....5935.....9835....15397.....23039 .15..238..1373...5032...14037...32802...67681...127310...222965....368920 .25..865..7377..35253..121117..336055..802125..1712987..3357255...6145113 .68.3417.41256.255821.1079992.3552027.9804610.23766209.52113718.105515163 LINKS R. H. Hardin, Table of n, a(n) for n = 1..165 EXAMPLE Some solutions for n=6 k=6 .-3...-4...-5...-4...-6...-6...-5...-6...-5...-4...-2...-4...-3...-5...-4...-6 .-3...-1....1...-2...-2....0....2....2...-2...-2...-2...-3...-1...-1....2...-1 ..0...-2...-1....4....3....4...-2....0....5...-1...-2....1....0....4...-1....2 ..4....2....2....4...-1....0....5....6....4...-3....2....2....2...-2....3...-2 ..4....5....0...-1....0....4...-5....2...-2....6...-1....2....4....5....1....5 .-2....0....3...-1....6...-2....5...-4....0....4....5....2...-2...-1...-1....2 CROSSREFS Row 3 is A028387(n-1) Sequence in context: A133913 A209485 A209344 * A141412 A178623 A210765 Adjacent sequences:  A209112 A209113 A209114 * A209116 A209117 A209118 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 05 2012 STATUS approved

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