A259250 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 0011 or 0111

9, 21, 21, 48, 65, 48, 111, 192, 192, 111, 255, 581, 720, 581, 255, 588, 1733, 2816, 2816, 1733, 588, 1353, 5216, 10720, 14425, 10720, 5216, 1353, 3117, 15613, 41552, 71313, 71313, 41552, 15613, 3117, 7176, 46897, 159168, 361728, 451481, 361728, 159168

Offset

1,1

Comments

Table starts

.....9.....21......48.......111........255..........588..........1353

....21.....65.....192.......581.......1733.........5216.........15613

....48....192.....720......2816......10720........41552........159168

...111....581....2816.....14425......71313.......361728.......1803859

...255...1733...10720.....71313.....451481......2964676......18970267

...588...5216...41552....361728....2964676.....25462352.....211569948

..1353..15613..159168...1803859...18970267....211569948....2259371001

..3117..46897..614560...9106657..123694345...1802996568...24946035357

..7176.140568.2360464..45601304..795726064..15090948960..268635598788

.16527.421901.9098240.229700941.5169185873.128059095616.2948447364239

Links

R. H. Hardin, Table of n, a(n) for n = 1..449

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +4*a(n-2) -11*a(n-3) -3*a(n-4)

k=3: a(n) = 2*a(n-1) +12*a(n-2) -11*a(n-3) -30*a(n-4)

k=4: [order 11]

k=5: [order 17]

k=6: [order 31]

k=7: [order 54]

Example

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

Crossrefs

Sequence in context: A218164 A161326 A250783 * A251219 A284131 A111171

Adjacent sequences: A259247 A259248 A259249 * A259251 A259252 A259253

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 22 2015

Status

approved