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Search: id:A003471
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| A003471 |
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Number of permutations with no hits on 2 main diagonals.
(Formerly M3525)
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+0
2
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| 1, 0, 0, 0, 4, 16, 80, 672, 4752, 48768, 440192, 5377280, 59245120, 839996160, 10930514688, 176547098112, 2649865335040, 48047352500224, 817154768973824, 16438490531536896, 312426715251262464, 6906073926286725120
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Permanent of the binary matrix with an entry equal to 0 iff the entry is on the main diagonal or the main antidiagonal. - Simone Severini (ss54(AT)york.ac.uk), Oct 14 2004
Comment from Toby Gottfried (toby(AT)gottfriedville.net), Dec 05 2008: (Start)
Suppose you have a group of married couples (plus perhaps one other person).
You wish to organize a gift exchange so that:
- each person gives and receives one gift.
- no one gives himself a gift.
- no one gives his/her spouse a gift.
Then the sequence gives the number of ways that this can be done. (End)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Hertzsprung, Losning og Udvidelse af Opgave 402, Tidsskrift for Math., 4 (1879), 134-140.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 187.
Simpson, Todd; Permutations with unique fixed and reflected points. Ars Combin. 39 (1995), 97-108.
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FORMULA
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a(n) = (n-1)*a(n-1) + 2*(n-d)*a(n-e), where (d, e) = (2, 4) if n even, (1, 2) if n odd.
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CROSSREFS
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Cf. A000166, A002777.
Sequence in context: A160564 A075581 A020080 this_sequence A002777 A118997 A001257
Adjacent sequences: A003468 A003469 A003470 this_sequence A003472 A003473 A003474
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Sep 24 2001
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