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A114209 Number of permutations of [n] having exactly two fixed points and avoiding the patterns 123 and 231. 2
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; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..67.

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, 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: A161051 A161255 A008731 * A132091 A262090 A239881

Adjacent sequences:  A114206 A114207 A114208 * A114210 A114211 A114212

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Nov 17 2005

STATUS

approved

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Last modified June 20 19:36 EDT 2019. Contains 324234 sequences. (Running on oeis4.)