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%I #9 Nov 21 2023 08:32:16
%S 1,1,2,7,37,272,2637,32469,493602,9062503,197409097,5027822588,
%T 147896295785,4972353491993,189357434418082,8104194176872583,
%U 387121098095180237,20513320778472547576,1199236185075846230469,76970026071431034905229,5399593095642890354948802
%N Number of (2+2)-free naturally labeled posets on [n].
%C A partial order R is naturally labeled if xRy => x<y.
%C A partial order is (2+2)-free if it does not contain an induced subposet that is isomorphic to the union of two disjoint 2-element chains.
%H David Bevan, Gi-Sang Cheon, and Sergey Kitaev, <a href="https://arxiv.org/abs/2311.08023">On naturally labelled posets and permutations avoiding 12-34</a>, arXiv:2311.08023 [math.CO], 2023.
%e a(3) = A006455(3) = 7: {}, {1R2}, {1R3}, {2R3}, {1R2, 1R3}, {1R3, 2R3}, {1R2, 1R3, 2R3}.
%e a(4) = A006455(4) - 3 = 37: {1R2, 3R4}, {1R3, 2R4} and {1R4, 2R3} (trivially) contain a 2+2 subposet.
%Y Cf. A006455 (naturally labeled posets), A113226 ({3,2+2}-free naturally labeled posets).
%K nonn
%O 0,3
%A _David Bevan_, Nov 20 2023