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Search: id:A114215
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| A114215 |
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Number of derangements of [n] avoiding the patterns 123, 132 and 213. |
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+0
1
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| 0, 1, 2, 4, 4, 9, 12, 25, 30, 64, 80, 169, 208, 441, 546, 1156, 1428, 3025, 3740, 7921, 9790, 20736, 25632, 54289, 67104, 142129, 175682, 372100, 459940, 974169, 1204140, 2550409, 3152478, 6677056, 8253296, 17480761, 21607408, 45765225
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OFFSET
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1,3
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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; Theorem 3.2.
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FORMULA
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a(n)=F(n)-F((n-2)/2)^2 if n is even; a(n)=F(n)-F((n-1)/2)^2 if n is odd; here F(n) is the Fibonacci sequence with F(0)=F(1)=1.
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EXAMPLE
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a(2)=1 because we have 21; a(3)=2 because we have 231 and 312; a(4)=4 because we have 3412,3421,4312 and 4321.
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MAPLE
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with(combinat): F:=n->fibonacci(n+1): a:=proc(n) if n mod 2 = 0 then F(n)-F((n-2)/2)^2 else F(n)-F((n-1)/2)^2 fi end: seq(a(n), n=1..45);
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CROSSREFS
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Sequence in context: A010464 A006579 A039887 this_sequence A151712 A038043 A126138
Adjacent sequences: A114212 A114213 A114214 this_sequence A114216 A114217 A114218
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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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