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%I #6 Apr 05 2020 21:10:45
%S 2,4,4,8,11,8,15,34,34,15,26,104,153,104,26,42,285,708,708,285,42,64,
%T 683,3013,4917,3013,683,64,93,1469,11292,33297,33297,11292,1469,93,
%U 130,2906,37312,204206,366606,204206,37312,2906,130,176,5383,110816,1108382
%N T(n,k) = Number of n X k 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X (k+1) binary array having two adjacent 1's and two adjacent 0's, with rows and columns of the latter in lexicographically nondecreasing order.
%C Table starts
%C ...2....4......8.......15.........26..........42..........64..........93
%C ...4...11.....34......104........285.........683........1469........2906
%C ...8...34....153......708.......3013.......11292.......37312......110816
%C ..15..104....708.....4917......33297......204206.....1108382.....5361624
%C ..26..285...3013....33297.....366606.....3774137....35026386...290742258
%C ..42..683..11292...204206....3774137....66730314..1084271645.15918049450
%C ..64.1469..37312..1108382...35026386..1084271645.31357593706
%C ..93.2906.110816..5361624..290742258.15918049450
%C .130.5383.301923.23477312.2174611745
%H R. H. Hardin, <a href="/A227333/b227333.txt">Table of n, a(n) for n = 1..97</a>
%F Empirical for column k:
%F k=1: a(n) = (1/6)*n^3 + (5/6)*n + 1.
%F k=2: [polynomial of degree 7] for n>2.
%F k=3: [polynomial of degree 15] for n>6.
%F k=4: [polynomial of degree 31] for n>10.
%e Some solutions for n=4, k=4
%e ..0..0..0..0....0..1..0..1....0..1..0..0....0..1..0..1....0..0..1..0
%e ..0..0..1..0....0..1..0..1....0..1..1..1....1..0..1..0....0..0..0..1
%e ..0..0..0..0....1..0..0..1....1..0..1..1....0..1..0..0....0..0..0..0
%e ..1..0..0..0....1..1..1..0....0..0..0..0....1..0..0..1....1..0..0..0
%Y Column 1 is A000125.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jul 07 2013
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