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

1,4

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000079(n-2)

Column 2 is A206687

Sequence in context: A282283 A288416 A240893 * A151706 A055372 A241078

Adjacent sequences: A241105 A241106 A241107 * A241109 A241110 A241111

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 16 2014

Status

approved