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%I #4 Jun 30 2013 14:14:21
%S 2,4,4,7,12,7,11,29,29,11,16,62,99,62,16,22,122,302,302,122,22,29,225,
%T 842,1339,842,225,29,37,393,2177,5517,5517,2177,393,37,46,655,5281,
%U 21335,34862,21335,5281,655,46,56,1048,12128,77706,210279,210279,77706,12128
%N T(n,k)=Number of nXk binary arrays indicating whether each 2X2 subblock of a larger binary array has lexicographically increasing rows and columns, for some larger (n+1)X(k+1) binary array with rows and columns of the latter in lexicographically nondecreasing order
%C Table starts
%C ..2....4.....7.....11.......16.........22..........29............37
%C ..4...12....29.....62......122........225.........393...........655
%C ..7...29....99....302......842.......2177........5281.........12128
%C .11...62...302...1339.....5517......21335.......77706........267130
%C .16..122...842...5517....34862.....210279.....1198995.......6435794
%C .22..225..2177..21335...210279....2016091....18423194.....158636376
%C .29..393..5281..77706..1198995...18423194...272856711....3820696108
%C .37..655.12128.267130..6435794..158636376..3820696108...87559140736
%C .46.1048.26548.868999.32506602.1281809749.50204897327.1887451154541
%H R. H. Hardin, <a href="/A227089/b227089.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
%F k=2: a(n) = (1/120)*n^5 + (1/24)*n^4 + (5/24)*n^3 + (35/24)*n^2 + (77/60)*n + 1
%F k=3: [polynomial of degree 11]
%F k=4: [polynomial of degree 23]
%F k=5: [polynomial of degree 47] for n>3
%e Some solutions for n=4 k=4
%e ..1..0..1..0....0..0..0..0....1..0..1..0....0..0..0..0....0..0..0..0
%e ..0..0..0..1....0..1..1..0....1..0..0..1....0..1..0..0....1..0..0..0
%e ..1..0..0..0....1..1..0..0....0..0..0..0....1..1..0..0....1..0..0..0
%e ..0..0..1..1....1..0..0..0....0..0..0..0....0..0..1..0....0..1..0..0
%Y Column 1 is A000124
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jun 30 2013
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