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%I #6 Apr 05 2020 21:15:17
%S 2,4,4,8,16,8,16,62,62,16,32,240,457,240,32,64,932,3346,3346,932,64,
%T 128,3620,24568,46126,24568,3620,128,256,14056,180575,636996,636996,
%U 180575,14056,256,512,54576,1327102,8802600,16517429,8802600,1327102,54576,512
%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.
%C Table starts
%C ...2......4........8..........16...........32............64...........128
%C ...4.....16.......62.........240..........932..........3620.........14056
%C ...8.....62......457........3346........24568........180575.......1327102
%C ..16....240.....3346.......46126.......636996.......8802600.....121623396
%C ..32....932....24568......636996.....16517429.....428106288...11089818502
%C ..64...3620...180575.....8802600....428106288...20779660903.1007348570226
%C .128..14056..1327102...121623396..11089818502.1007348570226
%C .256..54576..9752326..1680297950.287216470434
%C .512.211912.71665377.23214121178
%H R. H. Hardin, <a href="/A227442/b227442.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1).
%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +6*a(n-3).
%F k=3: [order 9].
%e Some solutions for n=4, k=4
%e ..1..0..1..1....0..0..0..0....1..0..1..1....1..0..0..0....0..1..1..0
%e ..1..0..1..0....1..1..0..1....0..1..0..0....0..0..0..0....0..0..0..1
%e ..1..0..0..1....1..1..1..0....1..0..0..1....0..0..0..0....0..0..1..1
%e ..1..1..1..1....1..1..1..0....1..0..0..0....0..1..0..0....0..1..0..0
%Y Column 1 is A000079.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jul 11 2013