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%I #4 Oct 28 2015 11:50:30
%S 2,2,2,3,2,3,3,3,3,3,4,3,7,3,4,4,4,7,7,4,4,5,4,14,7,14,4,5,5,5,14,16,
%T 16,14,5,5,6,5,25,17,61,17,25,5,6,6,6,25,41,93,93,41,25,6,6,7,6,41,48,
%U 494,379,494,48,41,6,7,7,7,41,113,975,2909,2909,975,113,41,7,7,8,7,63,141
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nondecreasing.
%C Table starts
%C .2.2..3...3.....4......4........5.........5.........6..........6.........7
%C .2.2..3...3.....4......4........5.........5.........6..........6.........7
%C .3.3..7...7....14.....14.......25........25........41.........41........63
%C .3.3..7...7....16.....17.......41........48.......113........141.......303
%C .4.4.14..16....61.....93......494.......975......4917......10340.....41366
%C .4.4.14..17....93....379.....2909.....20374....121878.....785046...3811314
%C .5.5.25..41...494...2909....62904....525967...8468941...71260394.850301770
%C .5.5.25..48...975..20374...525967..16701495.329866231.8672875293
%C .6.6.41.113..4917.121878..8468941.329866231
%C .6.6.41.141.10340.785046.71260394
%H R. H. Hardin, <a href="/A263873/b263873.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2) -a(n-3)
%F k=2: a(n) = a(n-1) +a(n-2) -a(n-3)
%F k=3: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7)
%F k=4: [order 14]
%F k=5: [order 37]
%F k=6: [order 79]
%e Some solutions for n=4 k=4
%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..1..1..1..1
%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..1..1..1..1
%e ..0..0..0..1..1....0..1..1..1..1....0..0..0..0..0....0..1..1..1..1
%e ..0..0..0..1..1....0..1..1..1..1....0..0..0..0..0....0..1..1..1..1
%Y Columns 1 and 2 are A004526(n+3).
%Y Column 3 is A263794(n+1).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Oct 28 2015
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