A208814 T(n,k)=Number of n-bead necklaces labeled with numbers -k..k not allowing reversal, with sum zero and three times sum of squares <= n*k*(k+1).

1, 1, 1, 1, 2, 3, 1, 3, 5, 4, 1, 3, 7, 15, 5, 1, 4, 13, 37, 59, 22, 1, 4, 19, 82, 185, 187, 37, 1, 5, 29, 141, 455, 982, 753, 62, 1, 5, 37, 236, 1093, 3375, 5491, 3125, 281, 1, 6, 43, 355, 2095, 8924, 22939, 30634, 12503, 558, 1, 7, 55, 499, 3595, 20409, 77053, 164311

Offset

1,5

Comments

Table starts

..1....1.....1......1......1.......1.......1........1........1........1

..1....2.....3......3......4.......4.......5........5........6........7

..3....5.....7.....13.....19......29......37.......43.......55.......67

..4...15....37.....82....141.....236.....355......499......698......949

..5...59...185....455...1093....2095....3595.....6075.....9505....13957

.22..187...982...3375...8924...20409...41962....77685...135150...223077

.37..753..5491..22939..77053..209793..486633..1041295..2015977..3665629

.62.3125.30634.164311.692566.2220143.5896400.14395011.31255834.62279783

Links

R. H. Hardin, Table of n, a(n) for n = 1..166

Example

Some solutions for n=6, k=5:
.-2...-4...-3...-3...-5...-4...-4...-4...-5...-3...-4...-5...-4...-4...-4...-5
.-2...-3...-2....0....0...-1....2....3....4....0...-4...-1....4....1....5...-3
..5....1....2...-2....1....2....0...-2....0...-3....2....1...-1...-1...-1....1
..0....1....1....0...-3...-2....0....2....0....5....3....1...-1...-2...-1....2
.-2....3...-2....1....4....3....5....4....0...-1....2....2....3....1....0....1
..1....2....4....4....3....2...-3...-3....1....2....1....2...-1....5....1....4

Crossrefs

Sequence in context: A243574 A121775 A127951 * A230449 A255437 A162609

Adjacent sequences: A208811 A208812 A208813 * A208815 A208816 A208817

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 01 2012

Status

approved