A228390 T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally or vertically.

1, 1, 1, 2, 2, 2, 3, 5, 5, 3, 5, 12, 21, 12, 5, 8, 29, 72, 72, 29, 8, 13, 70, 268, 382, 268, 70, 13, 21, 169, 963, 2104, 2104, 963, 169, 21, 34, 408, 3513, 11449, 17578, 11449, 3513, 408, 34, 55, 985, 12732, 62546, 143072, 143072, 62546, 12732, 985, 55, 89, 2378

Offset: 1

Author

R. H. Hardin Aug 21 2013

Keywords

• nonn
• tabl

Comments

Table starts

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

..1...2.....5......12.......29.........70..........169...........408

..2...5....21......72......268........963.........3513.........12732

..3..12....72.....382.....2104......11449........62546........341249

..5..29...268....2104....17578.....143072......1177709.......9646285

..8..70...963...11449...143072....1755243.....21683149.....267157140

.13.169..3513...62546..1177709...21683149....402968942....7458864720

.21.408.12732..341249..9646285..267157140...7458864720..207573951234

.34.985.46274.1862631.79185086.3294926929.138305554175.5784184947686

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1860

Crossrefs

Column 1 is A000045

Column 2 is A000129

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 4*a(n-1) +9*a(n-2) -5*a(n-3) -4*a(n-4) +a(n-5)

k=5: [order 9]

k=6: [order 11]

k=7: [order 21]