A066863 Number of binary arrangements without adjacent 1's on n X n staggered hexagonal grid.

2, 6, 43, 557, 14432, 719469, 70372090, 13351521479, 4941545691252, 3559349503024593, 4993739972681894885, 13642580224488264353504, 72582736229683196932680697, 751993955499337790653321567382, 15172223086707160824288341875907978

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 342-349.

J. Katzenelson and R. P. Kurshan, S/R: A Language for Specifying Protocols and Other Coordinating Processes, pp. 286-292 in Proc. IEEE Conf. Comput. Comm., 1986.

Links

Table of n, a(n) for n=1..15.

Steven R. Finch, Hard Square Entropy Constant [Broken link]

Steven R. Finch, Hard Square Entropy Constant [From the Wayback machine]

Sean A. Irvine, Java program (github)

Eric Weisstein's World of Mathematics, Hard Hexagon Entropy Constant

Example

Neighbors for n=4:
o--o--o--o
| /|\ | /|
|/ | \|/ |
o--o--o--o
| /|\ | /|
|/ | \|/ |
o--o--o--o
| /|\ | /|
|/ | \|/ |
o--o--o--o

Prog

[S/R] proc a
stvar $[N][N]:boolean
init $[][] := false
cyset true
asgn $[][]->{false, true}
kill +[i in 0.. N-1](
+[j in 0.. N-1](
$[i][j]`*(
($[i][j+1]`?(j<=N-2)|false)
+($[i-1][j-1]`?((i>0)*(j>0)*((j mod 2)=0))|false)
+($[i-1][j+1]`?((i>0)*(j<=N-2)*((j mod 2)=0))|false)
+($[i-1][j]`?(i>0)|false)))) end

Crossrefs

Cf. A006506, A027683, A066864, A066865, A066866.

Sequence in context: A198076 A330675 A183313 * A296828 A135815 A055564

Adjacent sequences: A066860 A066861 A066862 * A066864 A066865 A066866

Keyword

nonn

Author

R. H. Hardin, Jan 25 2002

Extensions

More terms from Sean A. Irvine, Nov 15 2023

Status

approved