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A129960
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Closed integer minimal solutions to: Solve[n!-m*(m-1)/2=0,m] Nearest SO(m) group below the symmetric group Sn in dimension.
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0
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1, 1, 2, 3, 6, 15, 37, 100, 283, 851, 2693, 8934, 30951, 111597, 417560, 1617203, 6468815, 26671611, 113158063, 493244564, 2205856753
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Algebriac variety sequence ( also not in OEIS) :dim=g#Sn-g#SO(n) low = a - c*(c - 1)/2 {1, 1, 1, 3, 9, 15, 54, 90, 417, 1205, 4022, 13089, 34875, 131394, 323180, 2404997, 9370295, 24764145, 151351047, 697679234, 1901716872}
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FORMULA
| a(n) = Round[Abs[m]] such that Solve[n!-m*(m-1)/2=0,m]
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EXAMPLE
| 24->S4->SO(6)->15: deta=9
120->S5->SO(15) ->105:delta=15
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MATHEMATICA
| a = Table[n!, {n, 0, 20}]; b = Table[m /. NSolve[a[[n]] - m*(m - 1)/2 == 0, m][[1]], {n, 1, Length[a]}]; c = Flatten[Round[Abs[b]]]
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CROSSREFS
| Sequence in context: A053561 A147773 A006403 * A115098 A036418 A120589
Adjacent sequences: A129957 A129958 A129959 * A129961 A129962 A129963
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 10 2007
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