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

%I A066866 #36 May 26 2024 12:51:38
%S A066866 1,5,22,201,4216,162314,12329633,1831137521,528106112383,
%T A066866 296848246952000,324932515409958655,692572885398506075946,
%U A066866 2874785146216927021053015,23237716875160177498526082523,365789982527236500400197753931927,11212996751916827855636781928754023265
%N A066866 Number of binary arrangements without adjacent 1's in n X n rhombic hexagonal grid torus.
%D A066866 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 342-349.
%D A066866 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 A066866 Sean A. Irvine, <a href="/A066866/b066866.txt">Table of n, a(n) for n = 1..18</a>
%H A066866 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/square/square.html">Hard Square Entropy Constant</a> [Broken link]
%H A066866 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 A066866 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a066/A066866.java">Java program</a> (github)
%H A066866 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p. 73.
%e A066866 neighbors for n=4:
%e A066866 .|/ |/ |/ |/
%e A066866 -o--o--o--o-
%e A066866 /| /| /| /|
%e A066866 .|/ |/ |/ |/
%e A066866 -o--o--o--o-
%e A066866 /| /| /| /|
%e A066866 .|/ |/ |/ |/
%e A066866 -o--o--o--o-
%e A066866 /| /| /| /|
%e A066866 .|/ |/ |/ |/
%e A066866 -o--o--o--o-
%e A066866 /| /| /| /|
%o A066866 (S/R) proc a
%o A066866 stvar $[N][N]:boolean
%o A066866 init $[][] := false
%o A066866 cyset true
%o A066866 asgn $[][]->{false,true}
%o A066866 kill +[i in 0.. N-1](
%o A066866 +[j in 0.. N-1](
%o A066866 $[i][j]`*(
%o A066866 $[i][(j+1) mod N]`
%o A066866 +$[(i-1) mod N][(j+1) mod N]`
%o A066866 +$[(i-1) mod N][j]` ))) end
%Y A066866 Cf. A006506, A027683, A066863, A066864, A066865.
%K A066866 nonn,hard
%O A066866 1,2
%A A066866 _R. H. Hardin_, Jan 25 2002
%E A066866 Terms a(11)-a(12) from _Vaclav Kotesovec_, May 07 2012
%E A066866 a(13) from _Vaclav Kotesovec_, Aug 15 2016
%E A066866 a(14) from _Vaclav Kotesovec_, May 24 2021
%E A066866 a(15)-a(16) from _Sean A. Irvine_, Nov 18 2023