A208945 T(n,k) = number of n-bead necklaces labeled with numbers -k..k not allowing reversal, with sum zero with no three beads in a row equal.

1, 1, 2, 1, 3, 2, 1, 4, 6, 5, 1, 5, 12, 22, 8, 1, 6, 20, 57, 68, 20, 1, 7, 30, 122, 274, 264, 38, 1, 8, 42, 223, 766, 1464, 988, 88, 1, 9, 56, 366, 1722, 5238, 7974, 3954, 196, 1, 10, 72, 563, 3376, 14430, 37044, 45050, 15980, 464, 1, 11, 90, 820, 6004, 33468, 125322, 270832

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

..2....6....12.....20......30......42.......56.......72.......90.......110

..5...22....57....122.....223.....366......563......820.....1143......1544

..8...68...274....766....1722....3376.....6004.....9928....15514.....23178

.20..264..1464...5238...14430...33468....68722...128844...225126....371858

.38..988..7974..37044..125322..344456...817362..1738516..3397474...6205668

.88.3954.45050.270832.1123612.3656654.10024344.24184890.52854218.106749960

Links

R. H. Hardin, Table of n, a(n) for n = 1..182

Example

Some solutions for n=5, k=5:
.-2...-5...-4...-3...-4...-4...-5...-5...-4...-3...-3...-5...-5...-5...-5...-4
..1....4...-1....1...-3...-2....4....3....0....3...-1....3....4....0...-5....2
..0...-1...-3...-1....1....4....3....4....3....1....1...-1....0....3....5....3
..2....4....5....2....2....3....0...-3....0....0....4....5....2...-2....3...-3
.-1...-2....3....1....4...-1...-2....1....1...-1...-1...-2...-1....4....2....2

Crossrefs

Row 3 is A002378.

Sequence in context: A361894 A066121 A039911 * A209073 A332077 A220901

Adjacent sequences: A208942 A208943 A208944 * A208946 A208947 A208948

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 03 2012

Status

approved