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A289717
The order of the semigroup of orientation-preserving or reserving partial transformations of n elements
1
1, 2, 9, 64, 549, 4566, 34711, 243944, 1622025, 10402858, 65219931, 403119036, 2469129229, 15032191422, 91123985023, 550590488656, 3318118088721, 19953003487314, 119759533521571, 717624299625188, 4293868352394261, 25658433286034662, 153142720988745159, 913049836619756664
OFFSET
0,2
COMMENTS
Note the typo in corollary 27 of Umar (the 2nd equal sign in the equation in the first line should be a plus).
LINKS
V. H. Fernandes, G. M. S. Gomes, M. M. Jesus, Congruences on monoids of transformations preserving the orientation on a finite chain, J. Alg. 321 (3) (2009) 743-757, proposition 1.10
A. Umar, Combinatorial Results for Semigroups of Orientation-Preserving Partial Transformations, J. Int. Seq. 14 (2011) # 11.7.5, corollary 27, Tables 3.1-3.3.
MAPLE
# Table 3.3 of Umar
A := proc(n, k)
if k = 0 then
1;
else
2*n*add(binomial(k-1, p-1)*binomial(n-1, p-1)*2^(n-p), p=1..k)-(n-1)*2^n-1-(k-1)*2^(n-1)*binomial(n, 2) ;
end if ;
end proc:
A289717 := proc(n)
add(A(n, k), k=0..n) ;
end proc:
CROSSREFS
Sequence in context: A052513 A216839 A024720 * A094100 A185897 A067297
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Sep 02 2017
STATUS
approved