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Search: id:A114210
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| A114210 |
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Number of derangements of [n] avoiding the patterns 123 and 231. |
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+0
3
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| 0, 1, 1, 3, 4, 7, 8, 14, 13, 23, 20, 34, 28, 48, 37, 64, 48, 82, 60, 103, 73, 126, 88, 151, 104, 179, 121, 209, 140, 241, 160, 276, 181, 313, 204, 352, 228, 394, 253, 438, 280, 484, 308, 533, 337, 584, 368, 637, 400, 693, 433, 751, 468, 811, 504, 874, 541, 939
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n)=binomial(n,2)+1-A114208(n)-A114209(n)
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REFERENCES
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T. Mansour and A. Robertson, Refined restricted permutations avoiding subsets of patterns of length three, Annals of Combinatorics, 6, 2002, 407-418.
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FORMULA
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(7n^2-18n+24)/24 if n mod 6 = 0; (n^2-1)/6 if n mod 6 = 1 or 5; (7n^2-18n+32)/24 if n mod 6 = 2 or 4; (n^2-3)/6 if n mod 6 = 3.
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EXAMPLE
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a(2)=1 because we have 21; a(3)=1 because we have 312; a(4)=3 because we have 2143, 4312, and 4321.
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MAPLE
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a:=proc(n) if n mod 6 = 0 then (7*n^2-18*n+24)/24 elif n mod 6 = 1 or n mod 6 = 5 then (n^2-1)/6 elif n mod 6 = 2 or n mod 6 = 4 then (7*n^2-18*n+32)/24 else (n^2-3)/6 fi end: seq(a(n), n=1..70);
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CROSSREFS
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Cf. A114208, A114209.
Adjacent sequences: A114207 A114208 A114209 this_sequence A114211 A114212 A114213
Sequence in context: A023054 A060023 A120355 this_sequence A073271 A117471 A112062
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 17 2005
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