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Search: id:A114208
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| A114208 |
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Number of permutations of [n] having exactly one fixed point and avoiding the patterns 123 and 231. |
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3
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| 1, 0, 3, 2, 6, 6, 12, 10, 21, 16, 31, 24, 44, 32, 60, 42, 77, 54, 97, 66, 120, 80, 144, 96, 171, 112, 201, 130, 232, 150, 266, 170, 303, 192, 341, 216, 382, 240, 426, 266, 471, 294, 519, 322, 570, 352, 622, 384, 677, 416, 735, 450, 794, 486, 856, 522, 921, 560
(list; graph; listen)
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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.
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FORMULA
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n^2/6 if n mod 6 = 0; (7*n^2-12*n+29)/24 if n mod 6 = 1 or 5; (n^2-4)/6 if n mod 6 = 2 or 4; (7*n^2-12*n+45)/24 if n mod 6 = 3.
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EXAMPLE
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a(2)=0 because none of the permutations 12 and 21 has exactly one fixed point;
a(3)=3 because we have 132, 213, and 321; a(4)=2 because we have 4132 and 4213.
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MAPLE
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a:=proc(n) if n mod 6 = 0 then n^2/6 elif n mod 6 = 1 or n mod 6 = 5 then (7*n^2-12*n+29)/24 elif n mod 6 = 2 or n mod 6 = 4 then (n^2-4)/6 else (7*n^2-12*n+45)/24 fi end: seq(a(n), n=1..70);
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CROSSREFS
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Cf. A114209, A114210.
Sequence in context: A023360 A096375 A062200 this_sequence A014686 A053090 A087237
Adjacent sequences: A114205 A114206 A114207 this_sequence A114209 A114210 A114211
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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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