A241108 T(n,k)=Number of nXk 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

1, 1, 1, 2, 4, 2, 4, 11, 11, 4, 8, 36, 58, 36, 8, 16, 116, 294, 294, 116, 16, 32, 376, 1522, 2436, 1522, 376, 32, 64, 1216, 7846, 19814, 19814, 7846, 1216, 64, 128, 3936, 40418, 162776, 259388, 162776, 40418, 3936, 128, 256, 12736, 208374, 1333934, 3374086

Offset: 1

Author

R. H. Hardin, Apr 16 2014

Keywords

• nonn
• tabl

Comments

Table starts

...1.....1.......2.........4...........8.............16...............32

...1.....4......11........36.........116............376.............1216

...2....11......58.......294........1522...........7846............40418

...4....36.....294......2436.......19814.........162776..........1333934

...8...116....1522.....19814......259388........3374086.........44030862

..16...376....7846....162776.....3374086.......70145916.......1454236806

..32..1216...40418...1333934....44030862.....1454236806......48054344508

..64..3936..208374..10937316...574246744....30189380016....1586763763374

.128.12736.1074002..89651534..7489718098...626548445696...52415988665902

.256.41216.5535686.734979136.97685897406.13004327687556.1731396543937826

Examples

			Some solutions for n=4 k=4
..0..1..1..2....0..1..1..2....0..1..2..0....0..1..0..2....0..1..2..0
..2..1..1..0....2..1..1..1....1..2..1..2....1..0..2..1....1..0..0..2
..1..0..2..1....0..2..1..1....2..1..2..0....2..1..1..0....2..0..0..0
..0..2..0..2....2..0..2..0....1..2..0..2....0..1..1..2....1..2..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..144

Crossrefs

Column 1 is A000079(n-2)

Column 2 is A206687

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) for n>2

k=2: a(n) = 2*a(n-1) +4*a(n-2) for n>4

k=3: a(n) = 3*a(n-1) +8*a(n-2) +16*a(n-3)

k=4: [order 10]

k=5: [order 26]

k=6: [order 76]