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Search: id:A112091
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| A112091 |
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Number of idempotent order-preserving partial transformations (of an n-element chain). |
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+0
1
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| 1, 2, 6, 21, 76, 276, 1001, 3626, 13126, 47501, 171876, 621876, 2250001, 8140626, 29453126, 106562501, 385546876, 1394921876, 5046875001, 18259765626, 66064453126
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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Laradji, A. and Umar, A. Combinatorial results for semigroups of order-preserving partial transformations. Journal of Algebra 278, (2004), 342-359.
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FORMULA
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a(n)= ((sqrt(5))^(n-1))*(((sqrt(5)+1)/2)^n-((sqrt(5)-1)/2)^n)); a(n)=1+5*(a(n-1)-a(n-2)), a(0)=1, a(1)=2
G.f.: (2x-1)^2/((1-x)(1-5x+5x^2)). Convolution of A081567 with the sequence 1,-1,-1,-1 (-1 continued). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 06 2008]
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EXAMPLE
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a(2) = 6 because there are exactly 6 idempotent order-preserving partial transformations (on a 2-element chain), namely: the empty map, (1)->(1), (2)->(2), (1,2)->(1,1), (1,2)->(1,2), (1,2)->(2,2)- the mappings are coordinate-wise
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CROSSREFS
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Sequence in context: A116809 A116819 A116782 this_sequence A108146 A116798 A116821
Adjacent sequences: A112088 A112089 A112090 this_sequence A112092 A112093 A112094
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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), Aug 25 2008
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