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T(n,k)=Number of (n+2)X(k+2) binary arrays with every 3X3 subblock commuting with each horizontal and vertical neighbor 3X3 subblock
10

%I #5 Mar 31 2012 12:36:19

%S 512,112,112,228,45,228,415,79,79,415,616,155,158,155,616,880,235,274,

%T 274,235,880,1205,295,362,458,362,295,1205,1508,355,430,578,578,430,

%U 355,1508,2008,423,506,670,834,670,506,423,2008,2793,531,610,790,970,970,790

%N T(n,k)=Number of (n+2)X(k+2) binary arrays with every 3X3 subblock commuting with each horizontal and vertical neighbor 3X3 subblock

%C Table starts

%C ..512.112..228..415..616..880.1205.1508.2008.2793..3776..5220..7274..9829.13345

%C ..112..45...79..155..235..295..355..423..531..740..1037..1434..1992..2706..3628

%C ..228..79..158..274..362..430..506..610..790.1094..1539..2128..2917..3951..5309

%C ..415.155..274..458..578..670..790..966.1242.1702..2338..3247..4460..6025..8139

%C ..616.235..362..578..834..970.1162.1418.1802.2446..3314..4446..6199..8432.11313

%C ..880.295..430..670..970.1230.1494.1834.2338.3142..4226..5674..7686.10543.14268

%C .1205.355..506..790.1162.1494.1910.2362.3002.4006..5390..7234..9790.13178.17955

%C .1508.423..610..966.1418.1834.2362.3018.3834.5122..6886..9242.12530.16874.22626

%C .2008.531..790.1242.1802.2338.3002.3834.5102.6794..9110.12238.16562.22266.29874

%C .2793.740.1094.1702.2446.3142.4006.5122.6794.9706.12930.17246.23194.31074.41542

%H R. H. Hardin, <a href="/A190033/b190033.txt">Table of n, a(n) for n = 1..5196</a>

%F Empirical for all columns: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) +a(n-6) -a(n-7) for n>11,10,11,12,13,14,15,16 respectively for k=1..8

%e Some solutions for 5X4

%e ..0..0..0..1....0..0..0..1....0..0..1..1....0..0..1..1....1..1..1..1

%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....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

%e ..1..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

%e ..1..1..0..0....0..0..0..0....0..0..0..1....0..0..0..0....1..1..1..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ May 04 2011