|
| |
|
|
A242429
|
|
Length of longest chain of nonempty proper subsemigroups of the monoid of partial injective order-preserving functions of a chain with n elements.
|
|
2
|
|
|
|
1, 5, 17, 53, 167, 550, 1899, 6809, 25067, 93902, 355775, 1358208, 5212573, 20082860, 77607895, 300638481, 1166999699, 4537960846, 17673418311, 68924837252, 269132082925, 1052055773292, 4116727946687, 16123827007348, 63205353550497, 247959367137320, 973469914150619, 3824345703033374, 15033634055076857
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
James Mitchell, Table of n, a(n) for n = 1..100
P. J. Cameron, M. Gadouleau, J. D. Mitchell, Y. Peresse, Chains of subsemigroups, arXiv preprint arXiv:1501.06394 [math.GR], 2015.
|
|
|
FORMULA
|
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
a(n) = binomial(2*n,n)/2 + 3*2^(n-1) - n - 2. - Gheorghe Coserea, May 16 2016
|
|
|
MATHEMATICA
|
a[n_] := Binomial[2n, n]/2 + 3*2^(n-1) - n - 2; Array[a, 30] (* Jean-François Alcover, Dec 15 2018, from PARI *)
|
|
|
PROG
|
(PARI) a(n)=-2-n+sum(i=0, n, binomial(n, i)*(binomial(n, i)+3)/2);
|
|
|
CROSSREFS
|
Cf. A227914, A242428.
Sequence in context: A048473 A154992 A178828 * A097160 A149656 A146063
Adjacent sequences: A242426 A242427 A242428 * A242430 A242431 A242432
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
James Mitchell, May 14 2014
|
|
|
STATUS
|
approved
|
| |
|
|
