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Search: id:A144224
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| A144224 |
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T(n,k) is the number of idempotent order-preserving full transformations (of an n-element chain) of waist k (waist(alpha) = max(Im(alpha))). |
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+0
1
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| 1, 1, 2, 1, 2, 5, 1, 2, 5, 13, 1, 2, 5, 13, 34, 1, 2, 5, 13, 34, 89, 1, 2, 5, 13, 34, 89, 233, 1, 2, 5, 13, 34, 89, 233, 610, 1, 2, 5, 13, 34, 89, 233, 610, 987, 1, 2, 5, 13, 34, 89, 233, 610, 987, 1597, 1, 2, 5, 13, 34, 89, 233, 610, 987, 1597, 2584, 1, 2, 5, 13, 34, 89, 233, 610
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OFFSET
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1,3
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REFERENCES
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Laradji, A. and Umar, A. Combinatorial results for semigroups of order-preserving full transformations. Semigroup Forum 72, (2006), 51-62.
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FORMULA
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T(n,k)=sum(j=1,k,C(k+j-1,j-1) for all n >=k.
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EXAMPLE
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T(4,3) = 5 because there are exactly 5 idempotent order-preserving full transformations (on a 4-element chain) of waist 3, namely: the five possible ordered images (1,1,3,3), (1,2,3,3), (1,3,3,3), (2,2,3,3), (3,3,3,3) of (1,2,3,4).
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CROSSREFS
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Sum of rows of T(n, k) is A001906(n+1) and T(n, k) = A001519(k+1) for all n>=k.
Sequence in context: A011404 A002211 A132309 this_sequence A122881 A135506 A068822
Adjacent sequences: A144221 A144222 A144223 this_sequence A144225 A144226 A144227
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KEYWORD
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nonn
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AUTHOR
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A. Umar (aumarh(AT)squ.edu.om), Sep 15 2008
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