A227751 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

2, 4, 4, 7, 13, 7, 13, 40, 40, 13, 24, 129, 210, 129, 24, 44, 409, 1122, 1122, 409, 44, 81, 1300, 6002, 10092, 6002, 1300, 81, 149, 4137, 32114, 90881, 90881, 32114, 4137, 149, 274, 13152, 171759, 817897, 1378923, 817897, 171759, 13152, 274, 504, 41825

Offset

1,1

Comments

Table starts

...2.....4.......7........13..........24............44...............81

...4....13......40.......129.........409..........1300.............4137

...7....40.....210......1122........6002.........32114...........171759

..13...129....1122.....10092.......90881........817897..........7363367

..24...409....6002.....90881.....1378923......20935625........317839952

..44..1300...32114....817897....20935625.....536234494......13732639679

..81..4137..171759...7363367...317839952...13732639679.....593219255593

.149.13152..918746..66282981..4824746883..351648537470...25621579279915

.274.41825.4914405.596664236.73241810146.9004763615933.1106648265092084

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) +a(n-3)

k=2: a(n) = a(n-1) +4*a(n-2) +8*a(n-3) +4*a(n-4) +a(n-5) -a(n-6)

k=3: [order 13]

k=4: [order 32]

Example

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

Crossrefs

Column 1 is A000073(n+3)

Sequence in context: A224158 A224409 A226870 * A268995 A205744 A237859

Adjacent sequences: A227748 A227749 A227750 * A227752 A227753 A227754

Keyword

nonn,tabl

Author

R. H. Hardin Jul 25 2013

Status

approved