A296643 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1, 2 or 4 neighboring 1s.

1, 2, 2, 4, 10, 4, 7, 28, 28, 7, 12, 86, 132, 86, 12, 21, 279, 671, 671, 279, 21, 37, 869, 3444, 5696, 3444, 869, 37, 65, 2728, 17558, 49872, 49872, 17558, 2728, 65, 114, 8596, 89613, 430522, 742601, 430522, 89613, 8596, 114, 200, 27004, 457188, 3713779

Offset

1,2

Comments

Table starts

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

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

...4....28.....132.......671........3444.........17558...........89613

...7....86.....671......5696.......49872........430522.........3713779

..12...279....3444.....49872......742601......10781621.......157255466

..21...869...17558....430522....10781621.....263456105......6468185511

..37..2728...89613...3713779...157255466....6468185511....267838310277

..65..8596..457188..32095222..2296958734..158971670482..11100574753607

.114.27004.2333009.277299810.33523275696.3904685293187.459672982178410

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

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 22]

k=4: [order 74]

Example

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

Crossrefs

Column 1 is A005251(n+2).

Column 2 is A296380.

Sequence in context: A121623 A267347 A296386 * A295040 A295531 A220259

Adjacent sequences: A296640 A296641 A296642 * A296644 A296645 A296646

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 17 2017

Status

approved