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%I #5 Mar 31 2012 12:37:00
%S 36,144,144,576,864,576,2304,5184,5184,2304,9216,31104,46656,31104,
%T 9216,36864,186624,419904,419904,186624,36864,147456,1119744,3779136,
%U 5738688,3779136,1119744,147456,589824,6718464,34012224,78428736,78428736
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that b(i,j)*b(i-1,j)-c(i,j)*c(i,j-1) is nonzero
%C Also 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements
%C Table starts
%C .....36......144........576.........2304...........9216............36864
%C ....144......864.......5184........31104.........186624..........1119744
%C ....576.....5184......46656.......419904........3779136.........34012224
%C ...2304....31104.....419904......5738688.......78428736.......1073134656
%C ...9216...186624....3779136.....78428736.....1631513664......34026967296
%C ..36864..1119744...34012224...1073134656....34026967296....1084257353088
%C .147456..6718464..306110016..14683622976...710001723456...34589078037504
%C .589824.40310784.2754990144.200937920832.14819050600704.1104253773912576
%H R. H. Hardin, <a href="/A204106/b204106.txt">Table of n, a(n) for n = 1..285</a>
%F Empirical for column k:
%F k=1: T(n,k)=4*T(n-1,k)
%F k=2: T(n,k)=6*T(n-1,k)
%F k=3: T(n,k)=9*T(n-1,k)
%F k=4: T(n,k)=15*T(n-1,k)-270*T(n-3,k)+324*T(n-4,k)
%F k=5: T(n,k)=25*T(n-1,k)-45*T(n-2,k)-963*T(n-3,k)+2025*T(n-4,k)+3645*T(n-5,k)-6561*T(n-6,k)
%F k=6: (order 15)
%F k=7: (order 45)
%e Some solutions for n=5 k=3
%e ..0..1..0..1....1..2..0..1....0..1..2..1....2..2..0..1....2..2..2..1
%e ..2..1..2..1....1..2..0..1....2..1..0..0....0..1..0..2....0..0..0..1
%e ..0..0..0..1....1..2..0..2....2..1..2..1....2..1..0..1....2..2..2..2
%e ..1..1..2..1....1..2..0..1....2..0..2..0....2..1..2..2....0..0..0..1
%e ..0..0..2..0....1..2..0..1....1..0..2..0....0..0..0..0....2..2..2..2
%e ..1..1..1..1....0..2..0..1....1..0..1..1....1..2..1..2....1..0..0..1
%Y Column 1 is A002063
%Y Column 2 is A067411(n+2)
%Y Column 3 is A055995(n+2)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 10 2012
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