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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).
9

%I #7 Mar 12 2017 23:15:03

%S 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,

%T 1,5,29,141,455,982,753,62,1,5,37,236,1093,3375,5491,3125,281,1,6,43,

%U 355,2095,8924,22939,30634,12503,558,1,7,55,499,3595,20409,77053,164311

%N 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).

%C Table starts

%C ..1....1.....1......1......1.......1.......1........1........1........1

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

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

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

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

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

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

%C .62.3125.30634.164311.692566.2220143.5896400.14395011.31255834.62279783

%H R. H. Hardin, <a href="/A208814/b208814.txt">Table of n, a(n) for n = 1..166</a>

%e Some solutions for n=6, k=5:

%e .-2...-4...-3...-3...-5...-4...-4...-4...-5...-3...-4...-5...-4...-4...-4...-5

%e .-2...-3...-2....0....0...-1....2....3....4....0...-4...-1....4....1....5...-3

%e ..5....1....2...-2....1....2....0...-2....0...-3....2....1...-1...-1...-1....1

%e ..0....1....1....0...-3...-2....0....2....0....5....3....1...-1...-2...-1....2

%e .-2....3...-2....1....4....3....5....4....0...-1....2....2....3....1....0....1

%e ..1....2....4....4....3....2...-3...-3....1....2....1....2...-1....5....1....4

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 01 2012