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Search: id:A089222
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| A089222 |
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Number of ways of sitting n people around a table for the second time without anyone sitting next to the same person as they did the first time. |
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+0
3
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| 0, 0, 0, 0, 10, 36, 322, 2832, 27954, 299260, 3474482, 43546872, 586722162, 8463487844, 130214368530, 2129319003680, 36889393903794, 675098760648204, 13015877566642418, 263726707757115400, 5603148830577775218
(list; graph; listen)
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OFFSET
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1,5
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REFERENCES
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J. Snell, Introduction to Probability, e-book, pp. 101 Q. 20.
Roberto Tauraso, The Dinner Table Problem: The Rectangular Case, INTEGERS, vol. 6 (2006), paper A11 (Note that in this paper a(1) = 1.)
Robert Tauraso, "The Dinner Table Problem: The Rectangular Case", Integers: Electronic Journal of Combinatorial Number Theory, Vol. 6 (2006), #A11. See Column 2 in the table on page 3.
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LINKS
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Charles M. Grinstead & J. Laurie Snell Introduction to Probability.
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EXAMPLE
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a(4)=0 because trying to arrange 1,2,3,4 around a table will always give a couple who is sitting next to each other and differ by 1.
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MATHEMATICA
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Same[cperm_, n_] := ( For[same = False; i = 2, (i <= n) && ! same, i++, same = ((Mod[cperm[[i - 1]], n] + 1) == cperm[[i]]) || ((Mod[cperm[[ i]], n] + 1) == cperm[[i - 1]])]; same = same || ((Mod[cperm[[n]], n] + 1) == cperm[[1]]) || ((Mod[ cperm[[1]], n] + 1) == cperm[[n]]); Return[same]); CntSame[n_] := (allPerms = Permutations[Range[n]]; count = 0; For[j = 1, j <= n!, j++, perm = allPerms[[j]]; If[ ! Same[perm, n], count++ ]]; Return[count]);
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CROSSREFS
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Cf. A002464.
Cf. A002816. [From Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 29 2009]
Sequence in context: A117327 A153371 A117404 this_sequence A139242 A139236 A096000
Adjacent sequences: A089219 A089220 A089221 this_sequence A089223 A089224 A089225
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KEYWORD
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nonn,new
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AUTHOR
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Udi Hadad (somebody(AT)netvision.net.il), Dec 22 2003
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EXTENSIONS
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Tauraso reference from Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Dec 21 2006
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 29 2009
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