This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A352212 #10 Mar 15 2022 05:23:17
%S A352212 1,1,3,6,10,15,21,36,60
%N A352212 Largest number of maximal triangle-free node-induced subgraphs of an n-node graph.
%C A352212 This sequence is log-superadditive, i.e., a(m+n) >= a(m)*a(n). By Fekete's subadditive lemma, it follows that the limit of a(n)^(1/n) exists and equals the supremum of a(n)^(1/n).
%C A352212 Assuming that there exists a disconnected optimal graph for n >= 8 (this is the case for n = 8 and n = 9), it would hold that a(10) = 100, a(11) = 150, a(12) = 225, and a(n) = 10*a(n-5) for n >= 13.
%F A352212 a(m+n) >= a(m)*a(n).
%F A352212 Limit_{n->oo} a(n)^(1/n) >= 10^(1/5) = 1.58489... .
%e A352212 For 2 <= n <= 7, a(n) = binomial(n,2) = A000217(n-1) and the complete graph is optimal (it is the unique optimal graph for 3 <= n <= 7), but a(8) = 36 > binomial(8,2), with the optimal graphs being K_4 + K_4, with up to 4 additional node-disjoint edges. For n = 9 the optimal graphs are K_4 + K_5 with up to 4 additional node-disjoint edges.
%Y A352212 Cf. A000217, A006785, A024607.
%Y A352212 For a list of related sequences, see cross-references in A342211.
%K A352212 nonn,more
%O A352212 1,3
%A A352212 _Pontus von Brömssen_, Mar 08 2022