A296386 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 or 2 neighboring 1s.

1, 2, 2, 4, 10, 4, 7, 28, 28, 7, 12, 86, 127, 86, 12, 21, 279, 641, 641, 279, 21, 37, 869, 3237, 5389, 3237, 869, 37, 65, 2728, 16248, 46786, 46786, 16248, 2728, 65, 114, 8596, 81661, 396806, 684894, 396806, 81661, 8596, 114, 200, 27004, 410199, 3372222

Offset

1,2

Comments

Table starts

...1.....2.......4.........7..........12............21..............37

...2....10......28........86.........279...........869............2728

...4....28.....127.......641........3237.........16248...........81661

...7....86.....641......5389.......46786........396806.........3372222

..12...279....3237.....46786......684894.......9703136.......138882856

..21...869...16248....396806.....9703136.....229596763......5498685275

..37..2728...81661...3372222...138882856....5498685275....221204933878

..65..8596..410199..28724880..1988460073..131626644289...8887761158698

.114.27004.2061212.244493344.28434977556.3147315906687.356576134627608

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) -a(n-2) +6*a(n-3) -6*a(n-4) +6*a(n-5) -5*a(n-6) +3*a(n-7) -a(n-8)

k=3: [order 16]

k=4: [order 40]

k=5: [order 92]

Example

Some solutions for n=5 k=4
..0..1..1..0. .0..0..0..0. .1..0..0..1. .0..1..0..1. .0..0..0..1
..0..0..0..0. .0..0..0..1. .1..1..0..1. .1..0..0..1. .0..1..1..0
..0..0..1..0. .0..0..0..1. .0..0..0..0. .1..1..0..0. .1..0..0..0
..0..1..0..1. .1..0..0..0. .0..1..1..0. .0..0..1..1. .1..0..0..0
..0..0..1..0. .1..1..0..0. .1..0..1..1. .0..0..0..0. .1..0..0..0

Crossrefs

Column 1 is A005251(n+2).

Sequence in context: A308434 A121623 A267347 * A296643 A295040 A295531

Adjacent sequences: A296383 A296384 A296385 * A296387 A296388 A296389

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 11 2017

Status

approved