%I A089222
%S A089222 0,0,0,0,10,36,322,2832,27954
%N A089222 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.
%D A089222 J. Snell, Introduction to Probability, e-book, pp. 101 Q. 20.
%D A089222 Roberto Tauraso, The Dinner Table Problem: The Rectangular Case, INTEGERS, 
               vol. 6 (2006), paper A11 (Note that in this paper a(1) = 1.)
%D A089222 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.
%H A089222 Charles M. Grinstead & J. Laurie Snell <a href="http://www.dartmouth.edu/
               ~chance/teaching_aids/books_articles/probability_book/book.html">
               Introduction to Probability</a>.
%e A089222 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.
%t A089222 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]);
%Y A089222 Cf. A002464.
%Y A089222 Sequence in context: A117327 A153371 A117404 this_sequence A139242 A139236 
               A096000
%Y A089222 Adjacent sequences: A089219 A089220 A089221 this_sequence A089223 A089224 
               A089225
%K A089222 nonn
%O A089222 1,5
%A A089222 Udi Hadad (somebody(AT)netvision.net.il), Dec 22 2003
%E A089222 Tauraso reference from Parthasarathy Nambi (PachaNambi(AT)yahoo.com), 
               Dec 21 2006