A385120 Number of fixed tree-like polyedges on the square lattice with n edges, rooted at a vertex.

1, 4, 18, 88, 435, 2184, 11018, 55888, 284229, 1448800, 7396290, 37804344, 193405121, 990177104, 5072380140, 25996758752, 133290312030, 683631234972, 3507250248422

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Ben Samberg, a(2) visualization

Ben Samberg, Python algorithm

Formula

a(n) = A308409(n) * (n+1). - Andrei Zabolotskii, Jul 02 2025

Example

a(0) = 1: empty structure.
a(1) = 4: a single vertical or horizontal edge, rooted at one of the two vertices.
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.

Crossrefs

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

Cf. A308409.

Sequence in context: A178577 A130524 A298646 * A199309 A083325 A050146

Adjacent sequences: A385117 A385118 A385119 * A385121 A385122 A385123

Keyword

nonn,more,hard

Author

Ben Samberg, Jun 18 2025

Extensions

a(13) corrected and a(15)-a(18) added by Falk Hüffner, May 25 2026

Status

approved