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%I #4 Jan 15 2014 06:56:02
%S 16,58,58,209,380,209,746,2481,2481,746,2660,15963,29130,15963,2660,
%T 9476,102683,337412,337412,102683,9476,33753,659235,3906424,7041734,
%U 3906424,659235,33753,120216,4232565,45143913,146785037,146785037,45143913
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the sum of each 2X2 subblock maximum and minimum lexicographically nondecreasing columnwise and nonincreasing rowwise
%C Table starts
%C ......16.........58..........209.............746...............2660
%C ......58........380.........2481...........15963.............102683
%C .....209.......2481........29130..........337412............3906424
%C .....746......15963.......337412.........7041734..........146785037
%C ....2660.....102683......3906424.......146785037.........5507798734
%C ....9476.....659235.....45143913......3054397001.......206338701948
%C ...33753....4232565....521746721.....63554803821......7729359642112
%C ..120216...27168327...6028565252...1322113787590....289479683332559
%C ..428160..174393813..69659874030..27503978998503..10841634018438254
%C .1524918.1119403274.804890692193.572147678579818.406031478000180997
%H R. H. Hardin, <a href="/A235736/b235736.txt">Table of n, a(n) for n = 1..179</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -6*a(n-3) +a(n-4) +2*a(n-5)
%F k=2: [order 13]
%F k=3: [order 34]
%F k=4: [order 86]
%e Some solutions for n=3 k=4
%e ..0..1..0..1..0....0..0..1..0..0....0..0..0..1..1....0..1..0..1..0
%e ..0..0..0..0..0....1..1..0..1..1....1..1..1..1..1....0..0..0..0..1
%e ..0..1..0..1..0....1..0..1..0..0....0..0..1..0..0....0..1..1..0..0
%e ..0..1..0..0..0....1..1..1..1..1....1..0..1..0..1....0..0..0..1..1
%Y Column 1 is A235510
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 15 2014
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