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%I #4 Jun 20 2013 11:29:58
%S 2,4,4,7,13,7,11,37,37,11,16,91,187,91,16,22,199,792,792,199,22,29,
%T 397,2866,6195,2866,397,29,37,736,9136,41222,41222,9136,736,37,46,
%U 1285,26267,235528,523701,235528,26267,1285,46,56,2134,69311,1179663,5692900
%N T(n,k)=Number of nXk (-1,0,1) arrays of determinants of 2X2 subblocks of some (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...13.....37.......91........199..........397...........736..........1285
%C ..7...37....187......792.......2866.........9136.........26267.........69311
%C .11...91....792.....6195......41222.......235528.......1179663.......5279390
%C .16..199...2866....41222.....523701......5692900......53537470.....442630782
%C .22..397...9136...235528....5692900....119835087....2182420206...34737998303
%C .29..736..26267..1179663...53537470...2182420206...77611438870.2412616653873
%C .37.1285..69311..5279390..442630782..34737998303.2412616653873
%C .46.2134.170084.21450391.3265819433.489248332852
%H R. H. Hardin, <a href="/A226870/b226870.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical: column k is a polynomial in n of degree 3*2^(k-1)-1 for k in 1..5 and n>0,0,1,5,13
%e Some solutions for n=4 k=4
%e ..0..0.-1..0....0..0..0..0....0..0.-1..1....0..0.-1..0....0.-1..1..0
%e ..0.-1.-1..0....0..0..0..0....0.-1..0..0....0.-1.-1..0....0..0..0..0
%e .-1..0..0..0...-1..1..0..0....0..0..0.-1...-1.-1..1..0....0..0..0..0
%e ..0..0..1..0....0..0..0..0....0..0..0..1....0..0..0..0...-1..1.-1..1
%Y Column 1 is A000124
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jun 20 2013