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 A352767 #6 Feb 16 2025 08:34:03
%S A352767 1,2,1,1,2,1,2,1,2,1,2,4,10
%N A352767 Number of n-node graphs with the maximum number (A352766(n)) of orientations.
%H A352767 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FanGraph.html">Fan Graph</a>
%H A352767 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HouseGraph.html">House Graph</a>
%H A352767 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SpiderGraph.html">Spider Graph</a>
%e A352767 For 1 <= n <= 13, the n-node graphs having A352766(n) orientations are listed below. Here, CU(G_1, ..., G_k) denotes the complement of the disjoint union of the graphs G_1, ..., G_k, P_m is the m-node path, and S(m_1, ..., m_k) denotes the spider graph with legs of lengths m_1, ..., m_k.
%e A352767 n = 1: P_1;
%e A352767 n = 2: P_2 and 2*P_1;
%e A352767 n = 3: P_3;
%e A352767 n = 4: CU(P_1, P_1, P_2) (the diamond graph);
%e A352767 n = 5: CU(P_1, P_4) (the fan graph F_{1,4}) and CU(P_1, P_1, P_3) (the house X-graph);
%e A352767 n = 6: CU(P_1, P_2, P_3);
%e A352767 n = 7: CU(P_1, P_2, P_4) and CU(P_1, P_1, P_2, P_3);
%e A352767 n = 8: CU(P_1, S(1, 2, 3));
%e A352767 n = 9: CU(P_1, P_1, S(1, 2, 3)) and CU(P_1, S(1, 2, 4));
%e A352767 n = 10: CU(P_1, P_2, S(1, 2, 3));
%e A352767 n = 11: CU(P_1, P_1, P_2, S(1, 2, 3)) and CU(P_1, P_2, S(1, 2, 4));
%e A352767 n = 12: CU(P_1, P_1, P_2, S(1, 2, 4)) and CU(P_1, P_2, T), where T is any of the three asymmetric trees on 9 nodes (S(1, 2, 5), S(1, 3, 4), or a 7-node path with two additional nodes joined to the 3rd and 4th node of the path, respectively);
%e A352767 n = 13: CU(P_1, P_2, P_3, S(1, 2, 3)), CU(P_1, P_1, P_2, T), where T is any of the three asymmetric trees on 9 nodes, and CU(P_1, P_2, T), where T is any of the six asymmetric trees on 10 nodes.
%Y A352767 Cf. A352766.
%K A352767 nonn,more
%O A352767 1,2
%A A352767 _Pontus von Brömssen_, Apr 02 2022