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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
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| 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
| T(n,k)=sum(j=1,k,C(k+j-1,j-1) for all n >=k.
Sum of rows of T(n, k) is A001906(n+1) and T(n, k) = A001519(k+1) for all n>=k.
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EXAMPLE
| 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).
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
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CROSSREFS
| Cf. A000045.
Sequence in context: A175011 A171840 A132309 * A122881 A135506 A068822
Adjacent sequences: A144221 A144222 A144223 * A144225 A144226 A144227
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KEYWORD
| nonn,tabl
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AUTHOR
| A. Umar (aumarh(AT)squ.edu.om), Sep 15 2008
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