A066866 Number of binary arrangements without adjacent 1's in n X n rhombic hexagonal grid torus.

1, 5, 22, 201, 4216, 162314, 12329633, 1831137521, 528106112383, 296848246952000, 324932515409958655, 692572885398506075946, 2874785146216927021053015, 23237716875160177498526082523, 365789982527236500400197753931927, 11212996751916827855636781928754023265

Offset

1,2

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

Sean A. Irvine, Table of n, a(n) for n = 1..18

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)

V. Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 73.

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]`*(
$[i][(j+1) mod N]`
+$[(i-1) mod N][(j+1) mod N]`
+$[(i-1) mod N][j]` ))) end

Crossrefs

Cf. A006506, A027683, A066863, A066864, A066865.

Sequence in context: A048252 A356773 A208804 * A115657 A066865 A183902

Adjacent sequences: A066863 A066864 A066865 * A066867 A066868 A066869

Keyword

nonn,hard

Author

R. H. Hardin, Jan 25 2002

Extensions

Terms a(11)-a(12) from Vaclav Kotesovec, May 07 2012

a(13) from Vaclav Kotesovec, Aug 15 2016

a(14) from Vaclav Kotesovec, May 24 2021

a(15)-a(16) from Sean A. Irvine, Nov 18 2023

Status

approved