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 A352214 #8 Mar 15 2022 05:23:37
%S A352214 1,1,1,4,7,11,23,44,71
%N A352214 Largest number of maximal claw-free node-induced subgraphs of an n-node graph.
%C A352214 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).
%F A352214 a(m+n) >= a(m)*a(n).
%F A352214 Limit_{n->oo} a(n)^(1/n) >= 71^(1/9) = 1.60581... .
%e A352214 All graphs with at most three nodes are claw-free, so a(n) = 1 for n <= 3 and any graph is optimal.
%e A352214 For 4 <= n <= 9, the following are all optimal graphs, i.e., graphs that have n nodes and a(n) maximal claw-free subgraphs:
%e A352214 n = 4: K_{1,3};
%e A352214 n = 5: K_{1,4};
%e A352214 n = 6: K_{1,5}, K_{3,3} with one edge removed, and K_{3,3};
%e A352214 n = 7: K_{3,4} with one edge removed;
%e A352214 n = 8: K_{4,4} with one edge removed;
%e A352214 n = 9: K_{4,5} with one edge removed.
%Y A352214 Cf. A022562, A086991.
%Y A352214 For a list of related sequences, see cross-references in A342211.
%K A352214 nonn,more
%O A352214 1,4
%A A352214 _Pontus von Brömssen_, Mar 08 2022