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Number of n-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n.
0

%I #11 Mar 20 2017 09:51:02

%S 1,2,4,23,187,2798,52208,1210780,32915700,1029158718,36366029268,

%T 1434017630862,62448855324545,2977529703278272,154305670613042906,

%U 8637641797383212010,519466811614545786362,33406493488132547194879,2287819864082225737308655,166242770253180661727941435

%N Number of n-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n.

%e Some solutions for n=6:

%e .-4...-6...-4...-3...-3...-2...-5...-4...-5...-3...-3...-5...-4...-6...-3...-4

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

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

%e ..4....3....4....3...-1...-2....3....5....0....1...-1....6....3....0....0....3

%e ..0....4...-1....0....1....1....2....0....5....4....2....3....4....6....4...-2

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

%Y Diagonal of A209032.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 04 2012

%E a(12)-a(20) from _Andrew Howroyd_, Mar 19 2017