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A060696
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Number of permutations in S_n avoiding the strings 123, 321 and 231.
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2
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1, 1, 2, 3, 5, 11, 23, 63, 153, 489, 1329, 4785, 14235, 56475, 181215, 780255, 2672145, 12348945, 44781345, 220253985, 840523635, 4370620275, 17465201775, 95498916975, 397983749625, 2278224696825, 9867844134225, 58917607974225
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(5)=11=4!!+3!!=2*4+1*3=(5-1)!!+(5-2)!!, for example.
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REFERENCES
| S. Kitaev, Multi-avoidance of generalized patterns, Discrete Math., 260 (2003), 89-100.
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FORMULA
| a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(n) = (n-2)a(n-2)+(n-3)!! for n >= 4
Exponential generating function for A(n)=a(n+1) (n>=0): (1+x)*exp(x^2/2)*(1+sqrt(Pi/2)*erf(x/sqrt(2))), where erf denotes the error function. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002
(n-1)!!+(n-2)!! (cf. A006882)
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CROSSREFS
| Cf. A011782.
Sequence in context: A173927 A176499 A175234 * A000628 A006888 A009589
Adjacent sequences: A060693 A060694 A060695 * A060697 A060698 A060699
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KEYWORD
| nonn
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AUTHOR
| Tuwani A. Tshifhumulo (tat(AT)univen.ac.za), Apr 20 2001
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EXTENSIONS
| Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 22 2001
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