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Number of (n+1)X7 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
1

%I #5 Mar 31 2012 12:37:00

%S 36864,1119744,34012224,1073134656,34026967296,1084257353088,

%T 34589078037504,1104253773912576,35260853693757696,

%U 1126080474692243328,35963576641587458304,1148590432691774845056,36683475387804277514496

%N Number of (n+1)X7 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

%H R. H. Hardin, <a href="/A204104/b204104.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 39*a(n-1) +117*a(n-2) -13419*a(n-3) +42120*a(n-4) +1465776*a(n-5) -7558272*a(n-6) -59591376*a(n-7) +389959596*a(n-8) +776691180*a(n-9) -7353962460*a(n-10) -230291100*a(n-11) +53356676400*a(n-12) -41452398000*a(n-13) -124357194000*a(n-14) +143489070000*a(n-15)

%e Some solutions for n=5

%e ..2..0..0..2..1..2..1....2..1..0..2..1..2..2....2..0..0..0..2..0..2

%e ..1..1..1..2..0..2..0....2..1..0..2..0..0..0....2..1..1..1..1..0..2

%e ..2..2..0..2..0..1..0....0..1..0..1..1..2..2....2..0..0..2..2..0..2

%e ..0..1..0..2..0..1..2....0..1..2..2..0..0..1....1..1..1..1..1..0..1

%e ..2..2..0..1..0..1..2....2..1..0..1..1..2..1....2..0..2..2..2..0..1

%e ..0..1..0..1..2..1..2....2..1..2..2..0..2..0....1..0..1..0..1..0..1

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 10 2012