A209115 T(n,k) = number of n-bead necklaces labeled 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.

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

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: A209485 A209344 A294099 * A353430 A353391 A141412

Adjacent sequences: A209112 A209113 A209114 * A209116 A209117 A209118

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 05 2012

Status

approved