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 A352216 #16 Mar 17 2022 23:58:59
%S A352216 1,1,1,4,7,11,21,36,62
%N A352216 Largest number of maximal diamond-free node-induced subgraphs of an n-node graph.
%C A352216 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 A352216 a(10) >= 102, because the complement of 2*C_5 has 102 maximal diamond-free subgraphs. It is likely that this is optimal.
%F A352216 a(m+n) >= a(m)*a(n).
%F A352216 Limit_{n->oo} a(n)^(1/n) >= 102^(1/10) = 1.58803... .
%e A352216 All graphs with at most three nodes are diamond-free, so a(n) = 1 for n <= 3 and any graph is optimal.
%e A352216 For 4 <= n <= 9, the following are all optimal graphs, i.e., graphs that have n nodes and a(n) maximal diamond-free subgraphs:
%e A352216 n = 4: the diamond graph;
%e A352216 n = 5: the wheel graph;
%e A352216 n = 6: the complement of the H graph, the complement of P_3 + P_3 (the disjoint union of two paths of length 2), and the octahedral graph;
%e A352216 n = 7: the complement of P_3 + P_4;
%e A352216 n = 8: the complement of P_3 + C_5, and the complement of 2*P_4;
%e A352216 n = 9: the complement of P_4 + C_5.
%Y A352216 Cf. A242790.
%Y A352216 For a list of related sequences, see cross-references in A342211.
%K A352216 nonn,more
%O A352216 1,4
%A A352216 _Pontus von Brömssen_, Mar 08 2022