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

Author

R. H. Hardin, Jun 22 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

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]