%I #18 Feb 16 2025 08:33:55
%S 1,1,2,6,18,106,819,10969
%N Number of connected graceful graphs on n vertices.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GracefulGraph.html">Graceful Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VertexCount.html">Vertex Count</a>
%F a(n) = A001349(n) - A308557(n). - _Pontus von Brömssen_, Dec 29 2024
%e 1 node: K_1
%e 2 nodes: P_2
%e 3 nodes: P_3, C_3
%e 4 nodes: K_1,3 (claw), K_4-e, P_4, paw graph, C_4, K_4
%e 5 nodes: K_2,3, K_1,1,3, K_1,1,1,2, P_5, S_5, W_5 (and 12 more)
%Y Cf. A001349, A308548 (not necessarily connected), A308557.
%K nonn,more,changed
%O 1,3
%A _Eric W. Weisstein_, Jun 06 2019
%E a(8) from _Eric W. Weisstein_, Aug 16 2019