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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..23.

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

Adjacent sequences:  A289714 A289715 A289716 * A289718 A289719 A289720

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Sep 02 2017

STATUS

approved

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Last modified August 3 07:58 EDT 2021. Contains 346435 sequences. (Running on oeis4.)