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Search: id:A145035
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| A145035 |
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T(n,k) is the number of order-decreasing and order-preserving partial transformations (of an n-chain) of waist k (waist(alpha) = max(Im(alpha))). |
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1
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| 1, 1, 1, 1, 3, 2, 1, 7, 8, 6, 1, 15, 24, 28, 22, 1, 31, 64, 96, 112, 90, 1, 63, 160, 288, 416, 484, 394, 1, 127, 384, 800, 1344, 1896, 2200, 1806
(list; table; graph; listen)
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OFFSET
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0,5
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REFERENCES
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Laradji, A. and Umar, A. Combinatorial results for semigroups of order-decreasing partial transformations. J. Integer Seq. 7, (2004), 04.3.8, 14 pp.
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LINKS
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Laradji, A. and Umar, A., Combinatorial Results for Semigroups of Order-Decreasing Partial Transformations , Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.8. [From A. Umar (aumarh(AT)squ.edu.om), Oct 07 2008]
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FORMULA
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T(n,k)=(n-k+1)sum(j=1,n,C(n,j)C(k+j-2,j-1))/n;
T(n,k)=2T(n-1,k)-T(n-1,k-1)+T(n,k-1), (n>=k>=1), T(n,0)=1, T(n,1)=-1+2^n.
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EXAMPLE
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T(3,2) = 8 because there are exactly 8 order-decreasing and order-preserving partial transformations (of a 3-chain) of waist 2, namely: 2->2, 3->2, (1,2)->(1,2), (1,3)->(1,2), (2,3)->(1,2), (2,3)->(2,2), (1,2,3)->(1,1,2), (1,2,3)->(1,2,2).
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CROSSREFS
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Row sums of T(n, k) is A006318
Sequence in context: A111960 A130462 A059380 this_sequence A122832 A056151 A134436
Adjacent sequences: A145032 A145033 A145034 this_sequence A145036 A145037 A145038
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KEYWORD
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nonn,tabl
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AUTHOR
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A. Umar (aumarh(AT)squ.edu.om), Sep 30 2008
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