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Number of partially ordered sets with no isolated points and with n "lines": pairs (a,b) where a < b and there is no c with a < c < b. The lines form the minimal basis for the partial ordering.
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%I #60 Nov 19 2024 05:24:00

%S 1,1,4,12,47,174,749,3291,15675,78104,411042,2261961,13009112,77860234

%N Number of partially ordered sets with no isolated points and with n "lines": pairs (a,b) where a < b and there is no c with a < c < b. The lines form the minimal basis for the partial ordering.

%C The points are unlabeled.

%D See A000112 for references and links about partially ordered sets.

%H N. J. A. Sloane, <a href="/A022016/a022016.jpg">Illustration of initial terms of A022016 and A022017</a>.

%e See Sloane's link.

%Y Cf. A000112, A022017, A342447.

%K nonn,more,changed

%O 0,3

%A _Franklin T. Adams-Watters_, Mar 30 2002

%E a(6)-a(13) from Rico Zöllner and _Konrad Handrich_, Nov 19 2024