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A066866
Number of binary arrangements without adjacent 1's in n X n rhombic hexagonal grid torus.
13
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
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
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