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Search: id:A062870
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| A062870 |
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Number of permutations of degree n with greatest sum of distances. |
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+0
2
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| 1, 1, 3, 4, 20, 36, 252, 576, 5184, 14400, 158400, 518400, 6739200, 25401600, 381024000, 1625702400, 27636940800, 131681894400, 2501955993600, 13168189440000, 276531978240000, 1593350922240000, 36647071211520000
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Number of possible values is 1,2,3,5,7,10,13,17,21,... which I conjecture to be A033638. Maximum distance divided by 2 is the same minus one, i.e. 0,1,2,4,6,9,12,16,20,... which seems to be A002620.
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LINKS
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Max Alekseyev, Proof of conjecture
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FORMULA
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Conjecture: a(n) = (n/2)!^2 if n is even else n*((n-1)/2)!^2, cf. A092186. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 21 2007. This is true, see link. - Max Alekseyev, Aug 21 2007
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EXAMPLE
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(4,3,1,2) has distances (3,1,2,2), sum is 8 and there are 3 other permutations of degree 4 {3, 4, 1, 2}, {3, 4, 2, 1}, {4, 3, 2, 1} with this sum which is the maximum possible.
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PROGRAM
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(PARI) for(k=0, 20, print1((2*k+1)*k!^2", "(k+1)!^2", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 27 2007
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CROSSREFS
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Cf. A062866, A062867, A062869, A002620.
Sequence in context: A051719 A047165 A124631 this_sequence A151419 A067281 A151357
Adjacent sequences: A062867 A062868 A062869 this_sequence A062871 A062872 A062873
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KEYWORD
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nonn
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com), Jun 26 2001
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EXTENSIONS
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a(10)-a(14) from Hugo Pfoertner (hugo(AT)pfoertner.org), Sep 23 2004
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 27 2007
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