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

1,2

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: A100296 A346818 A120758 * A179603 A298700 A215763

Adjacent sequences: A227911 A227912 A227913 * A227915 A227916 A227917

Keyword

nonn

Author

James Mitchell, Oct 13 2013

Status

approved