A289717 The order of the semigroup of orientation-preserving or reserving partial transformations of n elements

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

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