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Search: id:A136662
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| A136662 |
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Number of cycles of the permutations of [1,2,...,n], for n=1,2,3,... |
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+0
1
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| 1, 2, 1, 3, 2, 2, 1, 1, 2, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 5, 4, 4, 3, 3, 4, 4, 3, 3, 2, 2, 3, 3, 2, 4, 3, 3, 2, 2, 3, 3, 4, 2, 3, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 3, 2, 2, 1, 1, 2, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 3, 1, 2, 2, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The row lengths sequence is A000142(n), n>=1, (factorials).
The permutations of [1,2,...,n] are ordered in the standard way (lexicographic or numerically increasing). E.g. in Maple as permute(n) list for not too large n (around 10).
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LINKS
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W. Lang, First rows and cycle decompositions.
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FORMULA
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a(n,k)= number of cycles of the k-th permutation of [1,2,...,n] in standard (increasing) order.
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EXAMPLE
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[1];[2,1];[3,2,2,1,1,2];[4,3,3,2,2,3,3,2,2,1,1,2,2,1,3,2,2,1,1,2,2,3,1,2];...
Row n=3: permutations of [1,2,3] in the order [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]. Cycle decomposition: [[[1], [2], [3]], [[1], [2, 3]], [[1, 2], [3]], [[1, 2, 3]], [[1, 3, 2]], [[1, 3], [2]]]. Number of cycles: [3,2,2,1,1], the entries of row n=3.
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CROSSREFS
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Row sums (total cycle numbers) A000254.
Sequence in context: A021473 A035181 A035151 this_sequence A023595 A057515 A096852
Adjacent sequences: A136659 A136660 A136661 this_sequence A136663 A136664 A136665
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Feb 22 2008, May 21 2008
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