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%I #5 Mar 31 2012 12:36:05
%S 134217728,40922,40922,2175043,3383,2175043,5261909,16401,16401,
%T 5261909,21336430,339649,335092,339649,21336430,41303124,851259,
%U 1406478,1406478,851259,41303124,62806428,1119049,2074892,17616908,2074892,1119049
%N T(n,k)=Number of (n+2)X(k+2) 0..7 arrays with every 3X3 subblock commuting with each horizontal and vertical neighbor 3X3 subblock
%C Table starts
%C .134217728...40922..2175043..5261909..21336430..41303124..62806428..68281222
%C .....40922....3383....16401...339649....851259...1119049...1236313...1378665
%C ...2175043...16401...335092..1406478...2074892...2236060...2422316...3006844
%C ...5261909..339649..1406478.17616908..20944652..21482140..22417900..25486140
%C ..21336430..851259..2074892.20944652..59508492..60795484..64214956..70996220
%C ..41303124.1119049..2236060.21482140..60795484..69691980..76517148..87955372
%C ..62806428.1236313..2422316.22417900..64214956..76517148..93739724.120920668
%C ..68281222.1378665..3006844.25486140..70996220..87955372.120920668.178672908
%C .199303510.1968681..6080572.34731516..87664508.120673708.178469852.272599692
%C .384169510.5163488.15726572.73928044.167497324.228103324.325043020.550844092
%H R. H. Hardin, <a href="/A186574/b186574.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical, for all columns: a(n)=2*a(n-1)-a(n-2)+7*a(n-3)-14*a(n-4)+7*a(n-5)+7*a(n-6)-7*a(n-7) for n>26,12,11,12,13,14,15 respectively for k=1..7
%e Some solutions for 5X4
%e ..0..0..2..5....0..0..0..4....0..0..4..1....0..0..0..7....0..0..0..2
%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..6....0..0..0..0
%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e ..0..0..0..0....2..0..0..0....0..0..0..0....0..0..0..0....4..0..0..0
%e ..3..4..0..0....7..2..0..0....0..0..0..7....6..0..0..0....0..4..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 23 2011