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 A385120 #56 Jul 04 2025 17:19:47 %S A385120 1,4,18,88,435,2184,11018,55888,284229,1448800,7396290,37804344, %T A385120 193405121,990117104,5072380140 %N A385120 Number of fixed tree-like polyedges on the square lattice with n edges, rooted at a vertex. %H A385120 Ben Samberg, <a href="/A385120/a385120.png">a(2) visualization</a> %H A385120 Ben Samberg, <a href="/A385120/a385120_1.py.txt">Python algorithm</a> %F A385120 a(n) = A308409(n) * (n+1). - _Andrei Zabolotskii_, Jul 02 2025 %e A385120 a(0) = 1: empty structure. %e A385120 a(1) = 4: a single vertical or horizontal edge, rooted at one of the two vertices. %e A385120 a(2) = 18: six unrooted two-edge polyedges (a straight path oriented in 2 possible ways and an L-shaped path oriented in 4 possible ways), each rooted at one of the three vertices. %Y A385120 Cf. A096267 (not necessarily treelike), A056841 (free), A066158 (polyominoes). %Y A385120 Cf. A308409. %K A385120 nonn,more,hard %O A385120 0,2 %A A385120 _Ben Samberg_, Jun 18 2025