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

%I A066863 #20 Feb 16 2025 08:32:45
%S A066863 2,6,43,557,14432,719469,70372090,13351521479,4941545691252,
%T A066863 3559349503024593,4993739972681894885,13642580224488264353504,
%U A066863 72582736229683196932680697,751993955499337790653321567382,15172223086707160824288341875907978
%N A066863 Number of binary arrangements without adjacent 1's on n X n staggered hexagonal grid.
%D A066863 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 342-349.
%D A066863 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.
%H A066863 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/square/square.html">Hard Square Entropy Constant</a> [Broken link]
%H A066863 Steven R. Finch, <a href="http://web.archive.org/web/20010605012506/http://www.mathsoft.com/asolve/constant/square/square.html">Hard Square Entropy Constant</a> [From the Wayback machine]
%H A066863 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a066/A066863.java">Java program</a> (github)
%H A066863 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HardHexagonEntropyConstant.html">Hard Hexagon Entropy Constant</a>
%e A066863 Neighbors for n=4:
%e A066863 o--o--o--o
%e A066863 | /|\ | /|
%e A066863 |/ | \|/ |
%e A066863 o--o--o--o
%e A066863 | /|\ | /|
%e A066863 |/ | \|/ |
%e A066863 o--o--o--o
%e A066863 | /|\ | /|
%e A066863 |/ | \|/ |
%e A066863 o--o--o--o
%o A066863 [S/R] proc a
%o A066863 stvar $[N][N]:boolean
%o A066863 init $[][] := false
%o A066863 cyset true
%o A066863 asgn $[][]->{false,true}
%o A066863 kill +[i in 0.. N-1](
%o A066863 +[j in 0.. N-1](
%o A066863 $[i][j]`*(
%o A066863 ($[i][j+1]`?(j<=N-2)|false)
%o A066863 +($[i-1][j-1]`?((i>0)*(j>0)*((j mod 2)=0))|false)
%o A066863 +($[i-1][j+1]`?((i>0)*(j<=N-2)*((j mod 2)=0))|false)
%o A066863 +($[i-1][j]`?(i>0)|false)))) end
%Y A066863 Cf. A006506, A027683, A066864, A066865, A066866.
%K A066863 nonn
%O A066863 1,1
%A A066863 _R. H. Hardin_, Jan 25 2002
%E A066863 More terms from _Sean A. Irvine_, Nov 15 2023