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%I #19 Nov 16 2023 05:06:50
%S 2,6,43,557,14432,719469,70372090,13351521479,4941545691252,
%T 3559349503024593,4993739972681894885,13642580224488264353504,
%U 72582736229683196932680697,751993955499337790653321567382,15172223086707160824288341875907978
%N Number of binary arrangements without adjacent 1's on n X n staggered hexagonal grid.
%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 342-349.
%D 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 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/square/square.html">Hard Square Entropy Constant</a> [Broken link]
%H 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 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a066/A066863.java">Java program</a> (github)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HardHexagonEntropyConstant.html">Hard Hexagon Entropy Constant</a>
%e Neighbors for n=4:
%e o--o--o--o
%e | /|\ | /|
%e |/ | \|/ |
%e o--o--o--o
%e | /|\ | /|
%e |/ | \|/ |
%e o--o--o--o
%e | /|\ | /|
%e |/ | \|/ |
%e o--o--o--o
%o [S/R] proc a
%o stvar $[N][N]:boolean
%o init $[][] := false
%o cyset true
%o asgn $[][]->{false,true}
%o kill +[i in 0.. N-1](
%o +[j in 0.. N-1](
%o $[i][j]`*(
%o ($[i][j+1]`?(j<=N-2)|false)
%o +($[i-1][j-1]`?((i>0)*(j>0)*((j mod 2)=0))|false)
%o +($[i-1][j+1]`?((i>0)*(j<=N-2)*((j mod 2)=0))|false)
%o +($[i-1][j]`?(i>0)|false)))) end
%Y Cf. A006506, A027683, A066864, A066865, A066866.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 25 2002
%E More terms from _Sean A. Irvine_, Nov 15 2023
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