A227558 - OEIS

%I #4 Jul 16 2013 07:07:28

%S 2,4,4,7,12,7,11,33,33,11,16,81,147,81,16,22,179,585,585,179,22,29,

%T 362,2080,3939,2080,362,29,37,680,6653,23940,23940,6653,680,37,46,

%U 1201,19356,130231,256067,130231,19356,1201,46,56,2014,51827,635595,2474769,2474769

%N T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having nonzero determinant, 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...12.....33.......81........179..........362..........680.........1201

%C ..7...33....147......585.......2080.........6653........19356........51827

%C .11...81....585.....3939......23940.......130231.......635595......2807533

%C .16..179...2080....23940.....256067......2474769.....21404483....166020522

%C .22..362...6653...130231....2474769.....43380243....685331477...9693885819

%C .29..680..19356...635595...21404483....685331477..20073109783.528869530105

%C .37.1201..51827..2807533..166020522...9693885819.528869530105

%C .46.2014.129090.11342619.1163861138.123170298613

%H R. H. Hardin, <a href="/A227558/b227558.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: a(n) = (1/2)*n^2 + (1/2)*n + 1

%F k=2: a(n) = (1/40)*n^5 + (17/24)*n^3 + (34/15)*n + 1

%F k=3: [polynomial of degree 11]

%F k=4: [polynomial of degree 23] for n>5

%F k=5: [polynomial of degree 47] for n>13

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000124

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jul 16 2013