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A124188
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Number of 3-good permutations on {1,2,...,n}, i.e. permutations that contain each of the six patterns {123, 132, 213, 231, 312, 321} as a subsequence.
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0
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0, 0, 0, 0, 2, 218, 3070, 32972, 336196, 3533026, 39574122, 477773658, 6222603756, 87162325448, 1307616361026, 20922578066742, 355686650877778, 6402370841198538, 121645089807861208, 2432901968797138968, 51090942024922288784
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| A permutation of the integers {1,2,....,n} is k-good if each of the k! patterns on k integers is contained as a subsequence of the permutation. For example, with k=2, there are n!-2 permutations that contain both a "12" and a "21" pattern as a subsequence.
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FORMULA
| a(n) = n! -6*C(2*n,n)/(n+1) +5*2^n +4*C(n,2) -14*n -2*A000045(n+1) +20, n>4.
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EXAMPLE
| a(5) = 2 because 2 permutations of {1,2,3,4,5} are 3-good: (2,5,3,1,4), (4,1,3,5,2).
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MAPLE
| with (combinat):
a:= n-> `if` (n<5, 0, n! -6*binomial(2*n, n)/(n+1) +5*2^n +4*binomial(n, 2) -14*n -2*fibonacci(n+1) +20):
seq (a(n), n=1..30);
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CROSSREFS
| Sequence in context: A125058 A202741 A101393 * A078276 A117076 A037057
Adjacent sequences: A124185 A124186 A124187 * A124189 A124190 A124191
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KEYWORD
| nonn
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AUTHOR
| Nicole Holder, David Simpson and Anant Godbole (tertsu(AT)gmail.com), Dec 06 2006
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EXTENSIONS
| Edited by Alois P. Heinz (heinz(AT)hs-heilbronn.de), May 25 2011
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