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Search: id:A045611
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| A045611 |
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Number of different energy states of n positive and n negative charges on a necklace. Different sets of distances between n points chosen from 2n equally spaced points on a circle. |
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+0
5
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| 1, 1, 2, 3, 7, 13, 35, 85, 254, 701, 2377, 7944, 25220, 95910, 332300, 1164824
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Index entries for sequences related to necklaces
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EXAMPLE
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a(10) = 2377 because the multiplicities {1; 2; 5; 10; 20; 40; 60; 80; 120} occur {1; 1; 3; 22; 362; 1855; 1; 130; 2} times and 2377 = 1 + 1 + 3 + 22 + 362 + 1855 + 1 + 130 + 2. Total number of configurations = 1*1 + 1*2 + 3*5 + 22*10 + .. = 92378 (see C(2n + 1, n + 1)=A001700).
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MATHEMATICA
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n=4; perm=Permutations[ Table[ -1, {n-1} ]~Join~Table[ 1, {n} ] ]; res=Table[ (Prepend[ #, -1 ].RotateRight[ Prepend[ #, -1 ], k ])/2, {k, 1, n} ]&/@perm; kort=Length[ Length/@Split[ Sort[ res ] ] ]
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CROSSREFS
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For n=0..7 this is equal to A006840. Cf. A045610, A045611, A045612, A006840, A077078, A077079.
Sequence in context: A007827 A129859 A056953 this_sequence A006840 A123408 A033995
Adjacent sequences: A045608 A045609 A045610 this_sequence A045612 A045613 A045614
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KEYWORD
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nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be)
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