Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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