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 A352669 #22 Oct 13 2022 10:58:26
%S A352669 0,0,1,4,10,20,35,56,84,120,165,225
%N A352669 Maximum number of induced cycles in an n-node graph.
%C A352669 For 3 <= n <= 11, a(n) = binomial(n,3) = A000292(n-2) and the complete graph is the unique extremal graph, but a(12) = 225 > binomial(12,3), where the unique extremal graph is K_{6,6}.
%C A352669 Morrison and Scott (2017) prove that, for sufficiently large n (they say it ought to be true for n >= 30), a(n) = A276401(n), with the unique extremal graph being the empty cyclic braid graph with one cluster of size 4 if n == 1 (mod 3), one cluster of size 2 if n == 2 (mod 3), and all other clusters of size 3. (The empty cyclic braid graph is obtained by arranging clusters of nodes of the appropriate sizes in a cycle and joining all pairs of nodes in neighboring clusters with edges.) For 14 <= n <= 21, this graph is not extremal, because the balanced bipartite graph K_{floor(n/2),ceiling(n/2)} has A028723(n+1) > A276401(n) induced cycles.
%H A352669 Falk Hüffner, <a href="https://github.com/falk-hueffner/tinygraph">tinygraph</a>, software for generating integer sequences based on graph properties, version 43e7869.
%H A352669 Natasha Morrison and Alex Scott, <a href="http://dx.doi.org/10.1016/j.jctb.2017.03.007">Maximising the number of induced cycles in a graph</a>, Journal of Combinatorial Theory Series B 126 (2017), 24-61.
%Y A352669 Cf. A000292, A028723, A276401.
%Y A352669 Maximum number of induced copies of other graphs: A028723 (4-node cycle), A111384 (3-node path), A352665 (4-node path), A352666 (claw graph), A352667 (paw graph), A352668 (diamond graph).
%K A352669 nonn,hard,more
%O A352669 1,4
%A A352669 _Pontus von Brömssen_, Mar 26 2022
%E A352669 a(10)-a(12) added using tinygraph by _Falk Hüffner_, Apr 07 2022