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

1,1

Comments

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

Links

Table of n, a(n) for n=1..24.

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.

Example

_|_|_ is a polyedge with 5 edges

Crossrefs

Cf. A019988 for "free" polyedges, A348096.

6th row of A366767.

Sequence in context: A287223 A365246 A333080 * A150264 A294593 A214358

Adjacent sequences: A096264 A096265 A096266 * A096268 A096269 A096270

Keyword

nonn

Author

Alexander Malkis, Jun 22 2004

Extensions

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

Status

approved