Lieb's square ice constant

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Binary	1.10001010001000110100010111001100…
Decimal	1.539600717839002…
Hexadecimal	1.8A2345CC0442…
Continued fraction	$1 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{5 + \cfrac{1}{1 + \cfrac{1}{4 + \ddots}}}}}$

Lieb's square ice constant is a mathematical constant used in the field of combinatorics. It was introduced by Elliott H. Lieb in 1967. ^[1]

[edit] Definition

Let L denote the area of an n × n square lattice, where L = n² Assign a direction to each edge of the lattice. Denote the number of orientations of such that each vertex has two inwardly directed and two outwardly directled edges by ƒ(n).

$\lim_{n \to \infty}(f(n))^{n^{-2}}=\left(\frac{4}{3}\right)^\frac{3}{2}=\frac{8 \sqrt{3}}{9}=1.5396007\dots$