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%I #22 Mar 16 2021 09:16:13
%S 1,1,3,7,22,70,249,880,3238,12180,46247,174458,672920,2585414,10015955
%N Number of different energy states of n positive and n negative charges on a string.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a045/A045610.java">Java program</a>, GitHub.
%e For n=3 the 20 different arrangements of -1,-1,-1,1,1,1 result in 7 energy levels (sum of signed inverse distances):
%e {0,0,0,1,1,1},{1,1,1,0,0,0}: 13/10
%e {0,0,1,0,1,1},{1,1,0,1,0,0}: -41/30
%e {0,0,1,1,0,1},{0,1,0,0,1,1},{1,0,1,1,0,0},{1,1,0,0,1,0}: -56/30
%e {0,0,1,1,1,0},{0,1,1,1,0,0},{1,0,0,0,1,1},{1,1,0,0,0,1}: -8/10
%e {0,1,0,1,0,1},{1,0,1,0,1,0}: -37/10
%e {0,1,0,1,1,0},{0,1,1,0,1,0},{1,0,0,1,0,1},{1,0,1,0,0,1}: -89/30
%e {0,1,1,0,0,1},{1,0,0,1,1,0}: -71/30
%e so the multiplicities are 4*2 + 3*4 = 20 = binomial(6,3).
%t f[li_: {(0 | 1) ..}] := Outer[Times, 2 li - 1, 2 li - 1];
%t Table[Length @ Tally[Total[1/DeleteCases[f[#] DistanceMatrix[Range[2 n]], 0, 2], 2] & /@ Permutations[Join[Table[0, n], Table[1, n]]]], {n, 10}] (* _Wouter Meeussen_, Mar 15 2021 *)
%Y Cf. A045723.
%K nonn,more
%O 0,3
%A _Wouter Meeussen_
%E Corrected and extended by _Wouter Meeussen_, Mar 15 2021
%E a(12)-a(15) from _Sean A. Irvine_, Mar 15 2021
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