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%I #26 Nov 26 2023 08:37:06
%S 1,5,22,217,4726,164258,14840533,1834600977,669877863205,
%T 296979228487760,434542100979981567,692625866382651263578,
%U 4053364289624915167879497,23237986479606982160703729647,543749373021017146939376423644362,11213018647250714014261414954480048385
%N Number of binary arrangements without adjacent 1's on n X n staggered hexagonal torus bent for odd n.
%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]
%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 | /|\ | /|\
%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 /| /|\ | /|\ |\
%o (S/R)
%o 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 (
%o $[i][(j-1) mod N]`
%o +$[(i-1) mod N][j]`
%o +(
%o $[(i-1) mod N][(j-1) mod N]`
%o ? ((j mod 2)=0) |
%o $[(i+1) mod N][(j-1) mod N]`
%o )
%o ) ? ((j>0)+((N mod 2)=0)) | (
%o $[(i-1) mod N][j]`
%o +$[(i-1) mod N][(j-1) mod N]`
%o +$[(i+1) mod N][(j-1) mod N]` )))) end
%Y Cf. A006506, A027683, A066863, A066864, A066866, A067967 (shifted instead of bent).
%Y Row sums of A067015.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 25 2002
%E More terms from _Sean A. Irvine_, Nov 18 2023
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