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A227914 Length of longest chain of nonempty proper subsemigroups of the symmetric inverse monoid. 4
1, 6, 25, 116, 722, 5956, 59243, 667500, 8296060, 112406158, 1648441865, 26016230581, 439698829588, 7923291500266, 151636272041063, 3071397457222772, 65637064987470128, 1475783903907314842, 34822081020977308581, 860290584362463964031, 22206678791494395506940, 597775158911764084886982, 16751152450234618859184419, 487867395080603697285978385, 14745549219503008426659528806 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 1..200

P. J. Cameron, M. Gadouleau, J. D. Mitchell, Y. Peresse, Chains of subsemigroups, arXiv preprint arXiv:1501.06394 [math.GR], 2015.

O. Ganyushkin and I. Livinsky, Length of the inverse symmetric semigroup, Algebra Discrete Math., 12 (2011) 64-71.

MATHEMATICA

a[ n_] := Sum[ Binomial[ n, k] (Ceiling[3 k/2] - Total[IntegerDigits[ k, 2]] + 1) + Binomial[ Binomial[ n, k], 2] k! - 1, {k, n}]; (* Michael Somos, Feb 25 2014 *)

PROG

(PARI)

A007238(n) = ceil(3*n/2) - hammingweight(n) - 1;

a(n) = { sum(i = 1, n+1, my(Ni = binomial(n, i-1));

  Ni * (A007238(i-1) + 2) + Ni*(Ni-1)/2 * (i-1)! - 1) };

vector(25, n, a(n))  \\ Gheorghe Coserea, May 15 2016

CROSSREFS

Cf. A007238.

Sequence in context: A094669 A100296 A120758 * A179603 A298700 A215763

Adjacent sequences:  A227911 A227912 A227913 * A227915 A227916 A227917

KEYWORD

nonn

AUTHOR

James Mitchell, Oct 13 2013

STATUS

approved

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)