for .
Call two elements adjacent if they lie in positions and , and , or and for some . Call the number of such arrays with no pairs of adjacent 1s.
Equivalently, is the number of configurations of nonattacking kings
on an chessboard with regular hexagonal cells.
The first few values of for , 2, ... are 2, 6, 43, 557, 14432, ... (OEIS A066863).
Baxter, R. J. "Hard Hexagons: Exact Solution." J. Physics A13, 1023-1030, 1980.Baxter, R. J. Exactly
Solved Models in Statistical Mechanics. New York: Academic Press, 1982.Finch,
S. R. "Hard Square Entropy Constant." §5.12 in Mathematical
Constants. Cambridge, England: Cambridge University Press, pp. 342-349,
2003.Joyce, G. S. "On the Hard Hexagon Model and the Theory
of Modular Functions." Phil. Trans. Royal Soc. London A325, 643-702,
1988a.Joyce, G. S. "Exact Results for the Activity and Isothermal
Compressibility of the Hard-Hexagon Model." J. Phys. A: Math. Gen.21,
L983-L988, 1988b.Katzenelson, J. and Kurshan, R. P. "S/R:
A Language for Specifying Protocols and Other Coordinating Processes." In Proc.
IEEE Conf. Comput. Comm., pp. 286-292, 1986.Sloane, N. J. A.
Sequences A066863 and A085851
in "The On-Line Encyclopedia of Integer Sequences."