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%I #4 Jul 18 2013 21:40:27
%S 1,2,2,3,5,3,4,11,11,4,5,23,39,23,5,6,44,127,127,44,6,7,78,377,667,
%T 377,78,7,8,130,1014,3202,3202,1014,130,8,9,206,2518,13740,25241,
%U 13740,2518,206,9,10,313,5844,53575,179234,179234,53575,5844,313,10,11,459,12790
%N T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having determinant equal to one, with rows and columns of the latter in nondecreasing lexicographic order
%C Table starts
%C .1...2.....3......4........5..........6............7.............8
%C .2...5....11.....23.......44.........78..........130...........206
%C .3..11....39....127......377.......1014.........2518..........5844
%C .4..23...127....667.....3202......13740........53575........192191
%C .5..44...377...3202....25241.....179234......1147095.......6679750
%C .6..78..1014..13740...179234....2139328.....23032705.....224466940
%C .7.130..2518..53575..1147095...23032705....420651813....6956310972
%C .8.206..5844.192191..6679750..224466940...6956310972..196026480660
%C .9.313.12790.640831.35730988.1995242628.104620117266.5023590617706
%H R. H. Hardin, <a href="/A227641/b227641.txt">Table of n, a(n) for n = 1..143</a>
%F Empirical for column k:
%F k=1: a(n) = n
%F k=2: a(n) = (1/24)*n^4 - (1/12)*n^3 + (35/24)*n^2 - (29/12)*n + 4 for n>1
%F k=3: [polynomial of degree 9] for n>3
%F k=4: [polynomial of degree 19] for n>9
%F k=5: [polynomial of degree 39] for n>17
%e Some solutions for n=4 k=4
%e ..0..0..0..1....0..0..1..0....0..0..0..1....0..0..0..0....0..0..0..0
%e ..0..0..0..0....0..1..0..1....0..0..0..0....0..0..0..1....0..0..0..1
%e ..0..0..0..0....1..0..1..0....0..1..1..0....0..1..0..0....0..1..0..0
%e ..0..1..0..0....0..0..0..0....0..0..0..0....0..0..0..0....1..0..1..0
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Jul 18 2013
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