A096267 Number of fixed polyedges with n edges (number of ways of embedding connected undirected graphs with n edges into the plane square lattice, inequivalent up to translation).

2, 6, 22, 88, 372, 1628, 7312, 33466, 155446, 730534, 3466170, 16576874, 79810756, 386458826, 1880580352, 9190830700, 45088727820, 221945045488, 1095798917674, 5424898610958, 26922433371778, 133906343014110, 667370905196930, 3332257266746004

Offset: 1

Author

Alexander Malkis, Jun 22 2004

Keywords

• nonn

Comments

Found using the rooted method (also known as Redelmeier's algorithm).

Examples

			_|_|_ is a polyedge with 5 edges
		

Links

• Alexander Malkis, Polyedges, polyominoes and the 'Digit' game, diploma thesis in computer science, Universität des Saarlandes, 2003, Saarbrücken.
• Stephan Mertens and Cristopher Moore, Series expansion of the percolation threshold on hypercubic lattices, J. Phys. A: Math. Theor., 51 (2018), 475001. See Table 1.

Crossrefs

Cf. A019988 for "free" polyedges, A348096.

6th row of A366767.

Extensions

a(22)-a(24) from Mertens & Moore added by Andrey Zabolotskiy, Feb 01 2022