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A351100 Maximum number of 4-subsets of an n-set such that every 3-subset is covered at most twice.

%I A351100 #22 Oct 18 2022 13:05:02
%S A351100 2,5,9,15,28,40,60,80,108,143,182,225,280,340,405
%N A351100 Maximum number of 4-subsets of an n-set such that every 3-subset is covered at most twice.
%C A351100 Maximum number of K_4^3's that can be packed in a doubled K_n^3, where K_n^m is the complete m-uniform hypergraph on n vertices.
%H A351100 Richard K. Guy, <a href="/A001197/a001197.pdf">A problem of Zarankiewicz</a>, Research Paper No. 12, Department of Mathematics, University of Calgary, January 1967. [Annotated and scanned copy, with permission]
%H A351100 Haim Hanani, <a href="https://doi.org/10.4153/CJM-1960-013-3">On quadruple systems</a>, Canadian Journal of Mathematics, 12 (1960), 145-157.
%H A351100 Jeremy Tan, <a href="https://arxiv.org/abs/2203.02283">An attack on Zarankiewicz's problem through SAT solving</a>, arXiv:2203.02283 [math.CO], 2022.
%F A351100 a(n) >= 2*A001843(n). Equality holds if n = 6k+2 or 6k+4 (Hanani).
%e A351100 a(6) = 9 because of the following optimal collection of 4-subsets:
%e A351100   1 2 3 4
%e A351100   2 3 4 5
%e A351100   3 4 5 6
%e A351100   4 5 6 1
%e A351100   5 6 1 2
%e A351100   6 1 2 3
%e A351100   1 2 4 5
%e A351100   2 3 5 6
%e A351100   3 4 6 1
%Y A351100 Cf. A001839-A001843 for other packing sequences discussed in _Richard K. Guy_'s paper.
%K A351100 nonn,hard,more
%O A351100 4,1
%A A351100 _Jeremy Tan_, Jan 31 2022