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

1,4

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000045

Column 2 is A000129

Sequence in context: A322261 A304718 A036355 * A309256 A095972 A091974

Adjacent sequences: A228387 A228388 A228389 * A228391 A228392 A228393

Keyword

nonn,tabl

Author

R. H. Hardin Aug 21 2013

Status

approved