A208805 - OEIS

%I #7 Mar 13 2017 00:22:30

%S 1,1,1,1,2,2,1,3,4,3,1,3,5,11,3,1,4,8,24,33,15,1,4,12,50,99,105,22,1,

%T 5,17,84,239,518,395,38,1,5,22,136,561,1746,2782,1612,147,1,6,25,201,

%U 1073,4566,11557,15485,6323,296,1,7,31,278,1827,10372,38668,82577,88835,27727

%N T(n,k) = number of n-bead necklaces labeled with numbers -k..k 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.......1

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

%C ..2....4.....5.....8.....12......17......22......25.......31.......38......45

%C ..3...11....24....50.....84.....136.....201.....278......386......519.....670

%C ..3...33....99...239....561....1073....1827....3079.....4801.....7043...10225

%C .15..105...518..1746...4566...10372...21227...39191....68069...112194..176414

%C .22..395..2782.11557..38668..105147..243678..521213..1008722..1833875.3177066

%C .38.1612.15485.82577.347219.1111859.2951235.7202490.15635629.31151165

%H R. H. Hardin, <a href="/A208805/b208805.txt">Table of n, a(n) for n = 1..148</a>

%e Some solutions for n=6, k=2:

%e .-2...-2...-1...-2...-2...-2...-1...-2...-2...-1...-1...-2...-2...-1...-1...-2

%e ..0....0....0....1....0....1....0....1....1....0...-1....0...-1....0...-1....0

%e ..0....2....0...-1....0...-1....0...-1...-2...-1....1....1....1....1....0....1

%e ..0...-1....1...-1....0....0....0....1....1....0...-1...-1....1....0...-1....0

%e ..2....0....0....1....0....0...-1...-1....1....0....1....0....1...-1....1...-1

%e ..0....1....0....2....2....2....2....2....1....2....1....2....0....1....2....2

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 01 2012