|
Search: id:A000183
|
|
|
| A000183 |
|
Number of discordant permutations of length n.
(Formerly M2121 N0838)
|
|
+0
5
|
|
| 0, 0, 0, 1, 2, 20, 144, 1265, 12072, 126565, 1445100, 17875140, 238282730, 3407118041, 52034548064, 845569542593, 14570246018686, 265397214435860, 5095853023109484, 102877234050493609, 2178674876680100744
(list; graph; listen)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
a(n)=ways to reseat n diners at circular table, none in or next to original chair.
|
|
REFERENCES
|
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
Anthony C. Robin, Circular Wife Swapping, The Mathematical Gazette, November 2006.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Enumerative Combinatorics I, Example 4.7.17.
K. Yamamoto, Structure polynomial of Latin rectangles and its application to a combinatorial problem, Memoirs of the Faculty of Science, Kyusyu University, Series A, 10 (1956), 1-13.
|
|
FORMULA
|
a(n) = Sum_{m=0..n} (-1)^m*(n-m)!*A061702(n, m), n>2.
|
|
EXAMPLE
|
a(5)=2: [ 1 2 3 4 5 ] -> [ 3 4 5 1 2 ] or [ 4 5 1 2 3 ].
|
|
CROSSREFS
|
Cf. A061702, A061703, A000338, A000561-A000565.
Sequence in context: A003490 A003481 A081006 this_sequence A081159 A105489 A093302
Adjacent sequences: A000180 A000181 A000182 this_sequence A000184 A000185 A000186
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 18 2001
|
|
|
Search completed in 0.002 seconds
|
