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%I #5 Mar 31 2012 12:36:05
%S 19683,721,721,2917,173,2917,6594,401,401,6594,12122,1411,1399,1411,
%T 12122,20056,2617,3421,3421,2617,20056,29303,3379,4807,8983,4807,3379,
%U 29303,35198,4033,5605,11557,11557,5605,4033,35198,53611,4795,6511,12895
%N T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 3X3 subblock commuting with each horizontal and vertical neighbor 3X3 subblock
%C Table starts
%C .19683...721..2917..6594.12122.20056..29303..35198..53611..85029.121783.199305
%C ...721...173...401..1411..2617..3379...4033...4795...6361..10443..17153..26995
%C ..2917...401..1399..3421..4807..5605...6511...8029..11647..19237..31623..49805
%C ..6594..1411..3421..8983.11557.12895..14845..18415..25381..40279..63565.102591
%C .12122..2617..4807.11557.21007.23389..27391..33445..44263..68269.104335.154693
%C .20056..3379..5605.12895.23389.29935..36133..44887..60493..91519.137701.205879
%C .29303..4033..6511.14845.27391.36133..47719..60973..82447.122725.185863.278125
%C .35198..4795..8029.18415.33445.44887..60973..82783.112357.168727.255085.381007
%C .53611..6361.11647.25381.44263.60493..82447.112357.168391.250285.374335.562933
%C .85029.10443.19237.40279.68269.91519.122725.168727.250285.441199.644917.946087
%H R. H. Hardin, <a href="/A186568/b186568.txt">Table of n, a(n) for n = 1..1404</a>
%F Empirical, for all columns: a(n)=2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)+2*a(n-6)-2*a(n-7) for n>18,10,11,12,13,14,15,16 respectively for k=1..8
%e Some solutions for 5X4
%e ..0..0..1..0....0..0..0..1....0..0..0..1....0..0..0..0....1..0..0..0
%e ..2..0..0..1....0..0..0..0....0..0..0..1....0..0..0..0....0..0..0..0
%e ..0..2..0..0....0..0..0..0....0..0..0..1....1..0..0..0....0..0..0..0
%e ..0..0..2..0....1..0..0..0....0..0..0..1....2..1..0..0....0..0..0..0
%e ..0..0..0..2....0..0..0..2....0..0..0..1....1..2..1..0....0..1..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 23 2011
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