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A111589
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Triangle read by rows: number of idempotent order-preserving partial transformations (of an n-element totally ordered set) of width k (width(alpha) = |Dom(alpha)|).
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0
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1, 1, 1, 1, 2, 3, 1, 3, 9, 8, 1, 4, 18, 32, 21, 1, 5, 30, 80, 105, 55, 1, 6, 45, 160, 315, 330, 144, 1, 7, 63, 280, 735, 1155, 1008, 377
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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F(n,k)= C(n,k)*A001906(k-1), (n>=k>0),F(0,0)=1
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EXAMPLE
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F(3,2) = 9 because there are exactly 9 idempotent order-preserving partial transformations (on a 3-element chain) of width 2, namely: (1,2)->(1,1), (1,2)->(1,2), (1,2)->(2,2), (1,2)->(3,3), (1,3)->(1,1), (1,3)->(1,3),(1,3)->(3,3), (2,3)->(2,2), (2,3)->(2,3),( 2,3)->(3,3) - the mappings are coordinate-wise
Triangle begins:
1,
1,1,
1,2,3,
1,3,9,8,
1,4,18,32,21,
1,5,30,80,105,55,
1,6,45,160,315,330,144, ...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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