A227914 Length of longest chain of nonempty proper subsemigroups of the symmetric inverse monoid.

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

Offset: 1

Author

James Mitchell, Oct 13 2013

Keywords

• nonn

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.

Crossrefs

Cf. A007238.

Programs

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 *)

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