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A242432
Length of longest chain of nonempty proper subsemigroups of the monoid of partial injective orientation-preserving functions of a chain with n elements.
1
1, 6, 24, 92, 363, 1483, 6191, 26077, 109987, 462900, 1941613, 8115138, 33805905, 140413073, 581694265, 2404314784, 9917782935, 40837958578, 167889571658, 689231516287, 2825851058202, 11572537702747, 47342211484912, 193485587828057, 790066214186999, 3223470297388819, 13141840760544209, 53540833421980514
OFFSET
1,2
LINKS
P. J. Cameron, M. Gadouleau, J. D. Mitchell, Y. Peresse, Chains of subsemigroups, arXiv preprint arXiv:1501.06394 [math.GR], 2015.
MATHEMATICA
b[n_] := If[n < 1, 0, PrimeOmega[n]];
a[n_] := -2 - n + Sum[Binomial[n, i]*(b[i] + (Binomial[n, i] - 1)*i/2 + 2), {i, 0, n}];
Array[a, 28] (* Jean-François Alcover, Feb 19 2019, from PARI *)
PROG
(PARI) b(n)=if(n<1, 0, bigomega(n)) /* A001222 */
a(n)=-2-n+sum(i=0, n, binomial(n, i)*(b(i)+(binomial(n, i)-1)*i/2+2))
CROSSREFS
KEYWORD
nonn
AUTHOR
James Mitchell, May 14 2014
STATUS
approved