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

1,1

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

Links

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

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]

Example

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

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)

Sequence in context: A112922 A305077 A302175 * A133017 A371266 A290019

Adjacent sequences: A228680 A228681 A228682 * A228684 A228685 A228686

Keyword

nonn,tabl,look

Author

R. H. Hardin, Aug 30 2013

Status

approved