A251219 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having zero or two 1s

9, 21, 21, 49, 63, 49, 115, 191, 191, 115, 269, 589, 758, 589, 269, 631, 1807, 3089, 3089, 1807, 631, 1477, 5569, 12503, 16911, 12503, 5569, 1477, 3463, 17119, 50912, 91777, 91777, 50912, 17119, 3463, 8109, 52713, 206715, 502971, 666522, 502971, 206715

Offset

1,1

Comments

Table starts

.....9.....21.......49.......115.........269..........631...........1477

....21.....63......191.......589........1807.........5569..........17119

....49....191......758......3089.......12503........50912.........206715

...115....589.....3089.....16911.......91777.......502971........2746607

...269...1807....12503.....91777......666522......4907873.......35978029

...631...5569....50912....502971.....4907873.....48781920......482274751

..1477..17119...206715...2746607....35978029....482274751.....6424279907

..3463..52713...840931..15040763...264753513...4791965557....86110233175

..8109.162143..3417338..82261821..1945208633..47523048960..1151625700234

.19007.499081.13896689.450304289.14308155872.471984045011.15428988432635

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +4*a(n-2) -12*a(n-3) +4*a(n-5)

k=3: [order 9]

k=4: [order 16]

k=5: [order 32]

k=6: [order 62]

Example

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

Crossrefs

Sequence in context: A161326 A250783 A259250 * A284131 A111171 A317789

Adjacent sequences: A251216 A251217 A251218 * A251220 A251221 A251222

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 30 2014

Status

approved