cp's OEIS Frontend

A066865 Number of binary arrangements without adjacent 1's on n X n staggered hexagonal torus bent for odd n.

%I A066865 #26 Nov 26 2023 08:37:06
%S A066865 1,5,22,217,4726,164258,14840533,1834600977,669877863205,
%T A066865 296979228487760,434542100979981567,692625866382651263578,
%U A066865 4053364289624915167879497,23237986479606982160703729647,543749373021017146939376423644362,11213018647250714014261414954480048385
%N A066865 Number of binary arrangements without adjacent 1's on n X n staggered hexagonal torus bent for odd n.
%D A066865 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 342-349.
%D A066865 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 A066865 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/square/square.html">Hard Square Entropy Constant</a> [Broken link]
%H A066865 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 A066865 Neighbors for n=4:
%e A066865 \|/ | \|/ |
%e A066865 -o--o--o--o-
%e A066865  | /|\ | /|\
%e A066865 \|/ | \|/ |
%e A066865 -o--o--o--o-
%e A066865  | /|\ | /|\
%e A066865 \|/ | \|/ |
%e A066865 -o--o--o--o-
%e A066865  | /|\ | /|\
%e A066865 \|/ | \|/ |
%e A066865 -o--o--o--o-
%e A066865  | /|\ | /|\
%e A066865 Neighbors for n=5:
%e A066865 \|/ | \|/ | \|/
%e A066865  o--o--o--o--o
%e A066865 /| /|\ | /|\ |\
%e A066865 \|/ | \|/ | \|/
%e A066865  o--o--o--o--o
%e A066865 /| /|\ | /|\ |\
%e A066865 \|/ | \|/ | \|/
%e A066865  o--o--o--o--o
%e A066865 /| /|\ | /|\ |\
%e A066865 \|/ | \|/ | \|/
%e A066865  o--o--o--o--o
%e A066865 /| /|\ | /|\ |\
%e A066865 \|/ | \|/ | \|/
%e A066865  o--o--o--o--o
%e A066865 /| /|\ | /|\ |\
%o A066865 (S/R)
%o A066865 proc a
%o A066865 stvar $[N][N]:boolean
%o A066865 init $[][] := false
%o A066865 cyset true
%o A066865 asgn $[][]->{false,true}
%o A066865 kill +[i in 0.. N-1](
%o A066865 +[j in 0.. N-1](
%o A066865 $[i][j]`*(
%o A066865 (
%o A066865 $[i][(j-1) mod N]`
%o A066865 +$[(i-1) mod N][j]`
%o A066865 +(
%o A066865 $[(i-1) mod N][(j-1) mod N]`
%o A066865 ? ((j mod 2)=0) |
%o A066865 $[(i+1) mod N][(j-1) mod N]`
%o A066865 )
%o A066865 ) ? ((j>0)+((N mod 2)=0)) | (
%o A066865 $[(i-1) mod N][j]`
%o A066865 +$[(i-1) mod N][(j-1) mod N]`
%o A066865 +$[(i+1) mod N][(j-1) mod N]` )))) end
%Y A066865 Cf. A006506, A027683, A066863, A066864, A066866, A067967 (shifted instead of bent).
%Y A066865 Row sums of A067015.
%K A066865 nonn
%O A066865 1,2
%A A066865 _R. H. Hardin_, Jan 25 2002
%E A066865 More terms from _Sean A. Irvine_, Nov 18 2023