|
Search: id:A114209
|
|
|
| A114209 |
|
Number of permutations of [n] having exactly two fixed points and avoiding the patterns 123 and 231. |
|
+0
3
|
|
| 0, 1, 0, 2, 1, 3, 2, 5, 3, 7, 5, 9, 7, 12, 9, 15, 12, 18, 15, 22, 18, 26, 22, 30, 26, 35, 30, 40, 35, 45, 40, 51, 45, 57, 51, 63, 57, 70, 63, 77, 70, 84, 77, 92, 84, 100, 92, 108, 100, 117, 108, 126, 117, 135, 126, 145, 135, 155, 145, 165, 155, 176, 165, 187, 176, 198, 187
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
REFERENCES
|
T. Mansour and A. Robertson, Refined restricted permutations avoiding subsets of patterns of length three, Annals of Combinatorics, 6, 2002, 407-418.
|
|
FORMULA
|
n(n+6)/24 if n mod 6 = 0; (n^2-1)/24 if n mod 6 = 1 or 5; (n+2)(n+4)/24 if n mod 6 = 2 or 4; (n^2-9)/24 if n mod 6 = 3.
a(n)=A008731(n-2). O.g.f.: x^2/((1-x)^3(1+x)^2(1+x+x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 11 2008]
|
|
EXAMPLE
|
a(2)=1 because we have 12; a(3)=0 because no permutation of [3] can have exactly two fixed points; a(4)=2 because we have 1432 and 3214.
|
|
MAPLE
|
a:=proc(n) if n mod 6 = 0 then n*(n+6)/24 elif n mod 6 = 1 or n mod 6 = 5 then (n^2-1)/24 elif n mod 6 = 2 or n mod 6 = 4 then (n+2)*(n+4)/24 else (n^2-9)/24 fi end: seq(a(n), n=1..70);
|
|
CROSSREFS
|
Cf. A114208, A114210.
Sequence in context: A045747 A029138 A008731 this_sequence A132091 A051792 A053602
Adjacent sequences: A114206 A114207 A114208 this_sequence A114210 A114211 A114212
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 17 2005
|
|
|
Search completed in 0.002 seconds
|
