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Number of binary arrangements without adjacent 1's on n X n hexagonal staggered torus shifted for odd n.
1

%I #14 Nov 18 2023 22:24:09

%S 1,5,19,217,4076,164258,12285477,1834600977,527717587843,

%T 296979228487760,324881629286870822,692625866382651263578,

%U 2874716493700380888930840,23237986479606982160703729647,365788614113216462103977935612524,11213018647250714014261414954480048385

%N Number of binary arrangements without adjacent 1's on n X n hexagonal staggered torus shifted for odd n.

%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 342-349.

%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]

%e Neighbors for n=4:

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%e :-o--o--o--o-

%e : | /|\ | /|\

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%e :-o--o--o--o-

%e : | /|\ | /|\

%e :\|/ | \|/ |

%e :-o--o--o--o-

%e : | /|\ | /|\

%e :\|/ | \|/ |

%e :-o--o--o--o-

%e : | /|\ | /|\

%e Neighbors for n=5:

%e :\|/ | \|/ | \|

%e :-o--o--o--o--o-

%e : | /|\ | /|\ |\

%e :\|/ | \|/ | \|

%e :-o--o--o--o--o-

%e : | /|\ | /|\ |\

%e :\|/ | \|/ | \|

%e :-o--o--o--o--o-

%e : | /|\ | /|\ |\

%e :\|/ | \|/ | \|

%e :-o--o--o--o--o-

%e : | /|\ | /|\ |\

%e :\|/ | \|/ | \|

%e :-o--o--o--o--o-

%e : | /|\ | /|\ |\

%Y For bent instead of shifted for odd n see A066865.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 02 2002

%E More terms from _Sean A. Irvine_, Nov 18 2023