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Search: id:A127125
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| A127125 |
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Triangle read by rows: T(n,k) is the number of endofunctions on n objects where the multiset of loop sizes forms the k-th partition in Mathematica ordering. |
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2
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| 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 3, 3, 1, 2, 1, 1, 1, 1, 1, 1, 9, 6, 6, 3, 6, 3, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 20, 16, 16, 9, 15, 7, 4, 6, 4, 7, 3, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 48, 37, 37, 23, 41, 18, 11, 18, 9, 18, 7, 4, 7, 7, 7, 7, 7, 3, 1, 2, 2, 2, 1, 3, 2, 1, 2, 2, 1, 1, 1
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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The number of loops is equal to the number of components, but the sizes may be smaller.
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EXAMPLE
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For n = 3, the 7 endofunctions are (1,2,3) -> (1,1,1), (1,1,2), (1,2,1), (2,1,1), (1,2,3), (1,3,2), and (2,3,1). The loops are respectively 1, 1, 1|2, 12, 1|2|3, 1|23, and 123, corresponding to partitions [1], [1], [1^2], [2], [1^3], [2,1], and [3]. The partitions of 1 to 3 in Mma order are [1], [2], [1^2], [3], [2,1], and [1^3], so row 3 is 2, 1,1, 1,1,1.
The triangle starts:
1
1, 1 1
2, 1 1, 1 1 1
4, 3 3, 1 2 1, 1 1 1 1 1
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CROSSREFS
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Sequence in context: A129192 A062540 A115878 this_sequence A114171 A140345 A016024
Adjacent sequences: A127122 A127123 A127124 this_sequence A127126 A127127 A127128
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KEYWORD
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nonn,tabf
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 05 2007
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