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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 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 22:32 EST 2021. Contains 349468 sequences. (Running on oeis4.)