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%I #5 Mar 31 2012 12:36:05
%S 2401,1169,1169,17119,2923,17119,13411,5947,5947,13411,125368,26982,
%T 122034,26982,125368,110155,48875,75899,75899,48875,110155,878507,
%U 181792,877068,464292,877068,181792,878507,868467,349085,617557,696553,696553
%N T(n,k)=Number of (n+1)X(k+1) 0..6 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors
%C Table starts
%C ....2401....1169....17119.....13411....125368.....110155.....878507.....868467
%C ....1169....2923.....5947.....26982.....48875.....181792.....349085....1308972
%C ...17119....5947...122034.....75899....877068.....617557....6170249....5056121
%C ...13411...26982....75899....464292....696553....3225157....4596421...23135705
%C ..125368...48875...877068....696553...7513081....4754437...52753837...38012473
%C ..110155..181792...617557...3225157...4754437...24490909...30473221..176097889
%C ..878507..349085..6170249...4596421..52753837...30473221..378414577..236000977
%C ..868467.1308972..5056121..23135705..38012473..176097889..236000977.1358113549
%C .6231024.2606517.43638003..35032589.372605789..228669373.2684581153.1653455365
%C .6832034.9456818.40663383.165747519.310706825.1253936945.1947271657.9747375325
%H R. H. Hardin, <a href="/A186488/b186488.txt">Table of n, a(n) for n = 1..684</a>
%F Empirical, for every column: a(n)=2*a(n-1)+5*a(n-2)-12*a(n-3)+12*a(n-4)-6*a(n-5) for n>k+13
%e Some solutions for 4X3
%e ..4..0..0....2..0..5....3..0..0....2..3..0....6..1..0....0..5..4....0..0..3
%e ..3..0..0....0..2..0....2..0..0....4..0..3....2..0..1....0..0..5....0..0..0
%e ..0..3..0....5..0..2....0..2..0....0..4..0....0..2..0....0..0..0....1..0..0
%e ..3..0..3....0..5..1....4..0..2....6..0..4....6..0..2....0..0..0....6..1..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 22 2011
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