cp's OEIS Frontend

A242429 Length of longest chain of nonempty proper subsemigroups of the monoid of partial injective order-preserving functions of a chain with n elements.

%I A242429 #25 Dec 15 2018 15:26:14
%S A242429 1,5,17,53,167,550,1899,6809,25067,93902,355775,1358208,5212573,
%T A242429 20082860,77607895,300638481,1166999699,4537960846,17673418311,
%U A242429 68924837252,269132082925,1052055773292,4116727946687,16123827007348,63205353550497,247959367137320,973469914150619,3824345703033374,15033634055076857
%N A242429 Length of longest chain of nonempty proper subsemigroups of the monoid of partial injective order-preserving functions of a chain with n elements.
%H A242429 James Mitchell, <a href="/A242429/b242429.txt">Table of n, a(n) for n = 1..100</a>
%H A242429 P. J. Cameron, M. Gadouleau, J. D. Mitchell, Y. Peresse, <a href="http://arxiv.org/abs/1501.06394">Chains of subsemigroups</a>, arXiv preprint arXiv:1501.06394 [math.GR], 2015.
%F A242429 Conjecture: n*(131*n-376)*a(n) +2*(-563*n^2+1993*n-1185)*a(n-1) +3*(1099*n^2-4678*n+4684)*a(n-2) +2*(-1987*n^2+9803*n-12021)*a(n-3) +4*(209*n-387)*(2*n-7)*a(n-4)=0. - _R. J. Mathar_, Oct 20 2015
%F A242429 a(n) = binomial(2*n,n)/2 + 3*2^(n-1) - n - 2. - _Gheorghe Coserea_, May 16 2016
%t A242429 a[n_] := Binomial[2n, n]/2 + 3*2^(n-1) - n - 2; Array[a, 30] (* _Jean-François Alcover_, Dec 15 2018, from PARI *)
%o A242429 (PARI) a(n)=-2-n+sum(i=0, n, binomial(n,i)*(binomial(n,i)+3)/2);
%Y A242429 Cf. A227914, A242428.
%K A242429 nonn
%O A242429 1,2
%A A242429 _James Mitchell_, May 14 2014