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%I #5 Mar 31 2012 12:36:05
%S 625,419,419,3265,839,3265,3335,1715,1715,3335,17608,5879,17015,5879,
%T 17608,19617,10259,15061,15061,10259,19617,89163,28628,89650,64680,
%U 89650,28628,89163,110707,53045,85269,100789,100789,85269,53045,110707,459455
%N T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors
%C Table starts
%C ....625....419....3265....3335....17608....19617....89163....110707....459455
%C ....419....839....1715....5879....10259....28628....53045....150208....289063
%C ...3265...1715...17015...15061....89650....85269...453894....494751...2328714
%C ...3335...5879...15061...64680...100789...319970...489029...1667870...2708279
%C ..17608..10259...89650..100789...575344...510469..2895594...2857149..14788974
%C ..19617..28628...85269..319970...510469..1759744..2398869...9184194..12853549
%C ..89163..53045..453894..489029..2895594..2398869.15145144..13490069..77860794
%C .110707.150208..494751.1667870..2857149..9184194.13490069..52024944..69802869
%C .459455.289063.2328714.2708279.14788974.12853549.77860794..69802869.422063944
%C .624228.792360.2834305.8719842.16533319.47290374.77119949.270513394.391681269
%H R. H. Hardin, <a href="/A186484/b186484.txt">Table of n, a(n) for n = 1..647</a>
%F Empirical, for every column: a(n)=2*a(n-1)+3*a(n-2)-8*a(n-3)+8*a(n-4)-4*a(n-5) for n>k+11
%e Some solutions for 4X3
%e ..0..0..4....1..1..0....4..4..0....4..2..0....4..4..0....1..4..0....1..4..0
%e ..0..0..0....3..0..1....0..0..4....0..0..2....2..0..4....1..0..4....0..0..4
%e ..3..0..0....0..3..0....0..0..2....0..0..0....0..2..0....0..1..0....0..0..0
%e ..0..3..4....3..0..3....0..0..1....3..0..0....2..0..2....0..0..1....4..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 22 2011
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