A252695 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every consecutive three elements in every row and column having exactly two distinct values, and in every diagonal and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order

46, 96, 96, 148, 142, 148, 394, 204, 204, 394, 707, 519, 134, 519, 707, 1982, 1047, 407, 407, 1047, 1982, 3703, 2719, 291, 1480, 291, 2719, 3703, 10772, 6483, 881, 2048, 2048, 881, 6483, 10772, 20437, 16887, 727, 6246, 568, 6246, 727, 16887, 20437, 60042

Offset

1,1

Comments

Table starts

....46.....96..148....394...707...1982...3703...10772..20437...60042..115343

....96....142..204....519..1047...2719...6483...16887..42825..111655..288975

...148....204..134....407...291....881....727....2067...2067....5331....6491

...394....519..407...1480..2048...6246..12740...35128..84680..225000..573968

...707...1047..291...2048...568...4138...1276....8608...3244...18576....9144

..1982...2719..881...6246..4138..18940..25382...82842.168598..474106.1144322

..3703...6483..727..12740..1276..25382...2592...51060...5944..103716...15052

.10772..16887.2067..35128..8608..82842..51060..255112.337036.1125816.2286048

.20437..42825.2067..84680..3244.168598...5944..337036..12400..675756...28596

.60042.111655.5331.225000.18576.474106.103716.1125816.675756.3480808.4572432

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

Formula

Empirical for column k:

k=1: [linear recurrence of order 13] for n>14

k=2: [order 10] for n>11

k=3: [order 9] for n>10

k=4: [order 10] for n>11

k=5: [order 9] for n>10

k=6: [order 10] for n>11

k=7: [order 9] for n>10

Example

Some solutions for n=4 k=4
..0..1..0..1..0..1....0..1..0..1..0..1....0..1..1..2..2..1....0..1..1..0..0..1
..2..3..2..3..2..3....2..3..2..3..2..3....2..3..3..0..0..3....2..3..3..2..2..3
..2..3..2..3..2..3....2..3..2..3..2..3....2..1..1..2..2..3....2..1..1..0..0..1
..0..1..0..1..0..1....0..1..0..1..0..1....0..3..3..0..0..1....0..3..3..2..2..1
..0..1..0..1..0..1....0..1..0..1..0..1....2..1..1..2..2..1....2..1..1..0..0..3
..2..2..3..2..3..2....3..3..2..2..3..2....2..3..3..0..0..3....2..3..3..2..2..3

Crossrefs

Sequence in context: A260568 A044184 A044565 * A252688 A358897 A119417

Adjacent sequences: A252692 A252693 A252694 * A252696 A252697 A252698

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 20 2014

Status

approved