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%I #8 Jan 16 2014 14:06:43
%S 21,51,51,129,105,129,339,231,231,339,921,537,453,537,921,2571,1311,
%T 951,951,1311,2571,7329,3345,2109,1833,2109,3345,7329,21219,8871,4911,
%U 3759,3759,4911,8871,21219,62121,24297,11973,8097,7221,8097,11973,24297,62121
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2X2 subblock
%C Table starts
%C .....21.....51....129....339....921...2571...7329...21219...62121..183291
%C .....51....105....231....537...1311...3345...8871...24297...68271..195585
%C ....129....231....453....951...2109...4911..11973...30471...80589..220191
%C ....339....537....951...1833...3759...8097..18231...42873..105279..269457
%C ....921...1311...2109...3759...7221..14631..30909...67839..154821..368151
%C ...2571...3345...4911...8097..14631..28185..56751..118257..254391..566025
%C ...7329...8871..11973..18231..30909..56751.109893..220551..454989..963231
%C ..21219..24297..30471..42873..67839.118257.220551..429513..860559.1762017
%C ..62121..68271..80589.105279.154821.254391.454989..860559.1684821.3372711
%C .183291.195585.220191.269457.368151.566025.963231.1762017.3372711.6633465
%H R. H. Hardin, <a href="/A235884/b235884.txt">Table of n, a(n) for n = 1..390</a>
%F Empirical for diagonal and column k (the k=2 recurrence also works for k=1; apparently all rows and columns satisfy the same order 3 recurrence):
%F diagonal: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4)
%F k=1: a(n) = 5*a(n-1) -6*a(n-2)
%F k=2..7..(?): a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3)
%e Some solutions for n=5 k=4
%e ..0..0..0..0..0....2..1..1..2..2....2..2..2..2..1....1..1..0..1..1
%e ..0..0..0..0..0....1..2..2..1..1....2..2..2..2..1....1..1..0..1..1
%e ..2..2..2..2..2....1..2..2..1..1....1..1..1..1..2....1..1..0..1..1
%e ..2..2..2..2..2....1..2..2..1..1....1..1..1..1..2....0..0..1..0..0
%e ..1..1..1..1..1....1..2..2..1..1....2..2..2..2..1....1..1..0..1..1
%e ..1..1..1..1..1....1..2..2..1..1....2..2..2..2..1....0..0..1..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 16 2014
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