A228660 T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.

1, 1, 2, 2, 2, 4, 3, 8, 5, 8, 5, 14, 34, 12, 16, 8, 38, 78, 140, 29, 32, 13, 80, 335, 416, 574, 70, 64, 21, 194, 968, 2844, 2228, 2348, 169, 128, 34, 434, 3556, 11148, 24109, 11912, 9598, 408, 256, 55, 1016, 11245, 62368, 128740, 203762, 63688, 39224, 985, 512, 89

Offset: 1

Author

R. H. Hardin Aug 29 2013

Keywords

• nonn
• tabl

Comments

Table starts

...1...1......2.......3.........5..........8...........13............21

...2...2......8......14........38.........80..........194...........434

...4...5.....34......78.......335........968.........3556.........11245

...8..12....140.....416......2844......11148........62368........275708

..16..29....574....2228.....24109.....128740......1096624.......6780585

..32..70...2348...11912....203762....1482892.....19236832.....166237206

..64.169...9598...63688...1720343...17074988....337258048....4073313193

.128.408..39224..340480..14516920..196565912...5910459096...99770848656

.256.985.160282.1820208.122469941.2262692928.103561279328.2443423182349

Examples

			Some solutions for n=4 k=4
..1..0..0..1....1..0..0..0....1..0..0..1....1..0..1..0....1..0..0..1
..1..0..0..0....1..0..1..0....0..0..0..0....1..0..1..0....0..0..0..0
..0..0..0..0....1..0..1..0....0..0..0..0....1..0..1..0....0..0..1..0
..0..0..0..0....0..0..0..0....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(n-1)

Column 2 is A000129

Row 1 is A000045

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]