A066866 - OEIS

%I #36 May 26 2024 12:51:38

%S 1,5,22,201,4216,162314,12329633,1831137521,528106112383,

%T 296848246952000,324932515409958655,692572885398506075946,

%U 2874785146216927021053015,23237716875160177498526082523,365789982527236500400197753931927,11212996751916827855636781928754023265

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

%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 Sean A. Irvine, <a href="/A066866/b066866.txt">Table of n, a(n) for n = 1..18</a>

%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/A066866.java">Java program</a> (github)

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p. 73.

%e neighbors for n=4:

%e .|/ |/ |/ |/

%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-

%e /| /| /| /|

%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) mod N]`

%o +$[(i-1) mod N][(j+1) mod N]`

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

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

%K nonn,hard

%O 1,2

%A _R. H. Hardin_, Jan 25 2002

%E Terms a(11)-a(12) from _Vaclav Kotesovec_, May 07 2012

%E a(13) from _Vaclav Kotesovec_, Aug 15 2016

%E a(14) from _Vaclav Kotesovec_, May 24 2021

%E a(15)-a(16) from _Sean A. Irvine_, Nov 18 2023