A385120 - OEIS

%I #60 May 25 2026 11:09:37

%S 1,4,18,88,435,2184,11018,55888,284229,1448800,7396290,37804344,

%T 193405121,990177104,5072380140,25996758752,133290312030,683631234972,

%U 3507250248422

%N Number of fixed tree-like polyedges on the square lattice with n edges, rooted at a vertex.

%H Ben Samberg, <a href="/A385120/a385120.png">a(2) visualization</a>

%H Ben Samberg, <a href="/A385120/a385120_1.py.txt">Python algorithm</a>

%F a(n) = A308409(n) * (n+1). - _Andrei Zabolotskii_, Jul 02 2025

%e a(0) = 1: empty structure.

%e a(1) = 4: a single vertical or horizontal edge, rooted at one of the two vertices.

%e 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 Cf. A096267 (not necessarily treelike), A056841 (free), A066158 (polyominoes).

%Y Cf. A308409.

%K nonn,more,hard

%O 0,2

%A _Ben Samberg_, Jun 18 2025

%E a(13) corrected and a(15)-a(18) added by _Falk Hüffner_, May 25 2026