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 A045610 Number of different energy states of n positive and n negative charges on a string. 2
 1, 1, 3, 7, 22, 70, 249, 880, 3238, 12180, 46247, 174458, 672920, 2585414, 10015955 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Sean A. Irvine, Java program, GitHub. EXAMPLE For n=3 the 20 different arrangements of -1,-1,-1,1,1,1 result in 7 energy levels (sum of signed inverse distances): {0,0,0,1,1,1},{1,1,1,0,0,0}: 13/10 {0,0,1,0,1,1},{1,1,0,1,0,0}: -41/30 {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 {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 {0,1,0,1,0,1},{1,0,1,0,1,0}: -37/10 {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 {0,1,1,0,0,1},{1,0,0,1,1,0}: -71/30 so the multiplicities are 4*2 + 3*4 = 20 = binomial(6,3). MATHEMATICA f[li_: {(0 | 1) ..}] := Outer[Times, 2 li - 1, 2 li - 1]; 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 *) CROSSREFS Cf. A045723. Sequence in context: A319312 A325213 A148688 * A259809 A340022 A181769 Adjacent sequences:  A045607 A045608 A045609 * A045611 A045612 A045613 KEYWORD nonn,more AUTHOR EXTENSIONS Corrected and extended by Wouter Meeussen, Mar 15 2021 a(12)-a(15) from Sean A. Irvine, Mar 15 2021 STATUS approved

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Last modified May 19 05:04 EDT 2022. Contains 353826 sequences. (Running on oeis4.)