A227558 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

2, 4, 4, 7, 12, 7, 11, 33, 33, 11, 16, 81, 147, 81, 16, 22, 179, 585, 585, 179, 22, 29, 362, 2080, 3939, 2080, 362, 29, 37, 680, 6653, 23940, 23940, 6653, 680, 37, 46, 1201, 19356, 130231, 256067, 130231, 19356, 1201, 46, 56, 2014, 51827, 635595, 2474769, 2474769

Offset

1,1

Comments

Table starts

..2....4......7.......11.........16...........22...........29...........37

..4...12.....33.......81........179..........362..........680.........1201

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

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

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

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

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

.37.1201..51827..2807533..166020522...9693885819.528869530105

.46.2014.129090.11342619.1163861138.123170298613

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

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

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

k=3: [polynomial of degree 11]

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

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

Example

Some solutions for n=4 k=4
..0..0..1..0....0..1..0..0....0..0..1..0....0..0..1..0....0..0..0..0
..0..1..0..0....1..0..0..0....1..0..1..0....0..1..0..0....0..0..0..1
..0..1..0..0....0..1..0..1....0..0..0..0....0..1..0..1....0..0..1..0
..0..0..1..1....0..0..0..1....0..0..1..0....1..0..1..0....1..0..0..1

Crossrefs

Column 1 is A000124

Sequence in context: A223777 A227089 A225900 * A296651 A297085 A224158

Adjacent sequences: A227555 A227556 A227557 * A227559 A227560 A227561

Keyword

nonn,tabl

Author

R. H. Hardin Jul 16 2013

Status

approved