A227594 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

2, 4, 4, 8, 16, 8, 16, 64, 64, 16, 32, 256, 496, 256, 32, 64, 1024, 3840, 3840, 1024, 64, 128, 4096, 29676, 56928, 29676, 4096, 128, 256, 16384, 229140, 841984, 841984, 229140, 16384, 256, 512, 65536, 1768536, 12420672, 23778768, 12420672, 1768536

Offset

1,1

Comments

Table starts

...2......4.........8..........16.............32..............64

...4.....16........64.........256...........1024............4096

...8.....64.......496........3840..........29676..........229140

..16....256......3840.......56928.........841984........12420672

..32...1024.....29676......841984.......23778768.......668273468

..64...4096....229140....12420672......668273468.....35695226048

.128..16384...1768536...182940432....18728235880...1898924859202

.256..65536..13647884..2693032800...524299291340.100857512952616

.512.262144.105314460.39634170368.14670617834075

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 4*a(n-1)

k=3: [order 11]

k=4: [order 63]

Example

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

Crossrefs

Column 1 is A000079

Column 2 is A000302

Sequence in context: A189111 A181217 A223569 * A321241 A290128 A291778

Adjacent sequences: A227591 A227592 A227593 * A227595 A227596 A227597

Keyword

nonn,tabl

Author

R. H. Hardin Jul 17 2013

Status

approved