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%I #4 Nov 30 2014 07:13:54
%S 37,147,147,526,810,526,1844,3616,3616,1844,6544,15281,19131,15281,
%T 6544,23334,67518,99147,99147,67518,23334,83126,304870,549944,667626,
%U 549944,304870,83126,295938,1369052,3097574,4633551,4633551,3097574,1369052
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements
%C Table starts
%C ......37.......147........526........1844..........6544..........23334
%C .....147.......810.......3616.......15281.........67518.........304870
%C .....526......3616......19131.......99147........549944........3097574
%C ....1844.....15281......99147......667626.......4633551.......32006770
%C ....6544.....67518.....549944.....4633551......39326009......336432413
%C ...23334....304870....3097574....32006770.....336432413.....3656310083
%C ...83126...1369052...17154384...219945737....2909254399....39932445704
%C ..295938...6118942...94541640..1519227598...25213072536...430092324035
%C .1053609..27356256..523362695.10534571961..217873020830..4617478843871
%C .3751373.122402144.2902098174.72985741167.1882537978094.49985974667101
%H R. H. Hardin, <a href="/A251113/b251113.txt">Table of n, a(n) for n = 1..364</a>
%F Empirical for column k:
%F k=1: a(n) = 5*a(n-1) -8*a(n-2) +13*a(n-3) -12*a(n-4) +9*a(n-5) -5*a(n-6) +a(n-7)
%F k=2: [order 14]
%F k=3: [order 26] for n>27
%F k=4: [order 52] for n>54
%e Some solutions for n=3 k=4
%e ..1..0..1..2..2....0..1..1..1..2....0..0..0..0..0....1..0..1..0..2
%e ..1..0..1..0..1....1..0..0..0..1....1..0..0..0..0....2..0..1..0..1
%e ..1..0..1..1..0....1..0..0..0..1....1..1..1..0..0....2..0..1..0..1
%e ..2..0..0..1..0....2..2..2..2..0....2..0..1..1..0....2..0..1..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 30 2014
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