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 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

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Last modified March 25 09:47 EDT 2023. Contains 361520 sequences. (Running on oeis4.)