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

1,3

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

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
..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

Crossrefs

Column 1 is A000079(n-1)

Column 2 is A000129

Row 1 is A000045

Sequence in context: A210596 A240078 A344789 * A228796 A155837 A096445

Adjacent sequences: A228657 A228658 A228659 * A228661 A228662 A228663

Keyword

nonn,tabl

Author

R. H. Hardin Aug 29 2013

Status

approved