A228683 T(n,k)=Number of nXk binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.

2, 3, 4, 5, 7, 8, 8, 19, 17, 16, 13, 40, 77, 41, 32, 21, 97, 216, 313, 99, 64, 34, 217, 809, 1152, 1277, 239, 128, 55, 508, 2529, 6737, 6160, 5215, 577, 256, 89, 1159, 8832, 28977, 56549, 32928, 21305, 1393, 512, 144, 2683, 28793, 152048, 333517, 475809, 176032

Offset: 1

Author

R. H. Hardin Aug 30 2013

Keywords

• nonn
• tabl
• look

Comments

Table starts

...2....3......5.......8........13.........21...........34............55

...4....7.....19......40........97........217..........508..........1159

...8...17.....77.....216.......809.......2529.........8832.........28793

..16...41....313....1152......6737......28977.......152048........699833

..32...99...1277....6160.....56549.....333517......2644336......17124415

..64..239...5215...32928....475809....3837761.....46125216.....419022831

.128..577..21305..176032...4008817...44171841....806190208...10258304689

.256.1393..87049..941056..33795201..508425617..14105294112..251170142257

.512.3363.355685.5030848.284980061.5852202757.246929287360.6150224353031

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1057

Crossrefs

Column 1 is A000079

Column 2 is A001333(n+1)

Diagonal is A067963

Row 1 is A000045(n+2)

Row 2 is A006130(n+1)

Formula

Empirical for column k:

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

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

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

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

k=5: a(n) = 12*a(n-1) -27*a(n-2) -32*a(n-3) +49*a(n-4) +20*a(n-5) -5*a(n-6)

k=6: [order 7]

k=7: [order 12]

Empirical for row n:

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

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

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

n=4: a(n) = 2*a(n-1) +16*a(n-2) -7*a(n-3) -18*a(n-4)

n=5: [order 7]

n=6: [order 10]

n=7: [order 16]