A283282 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal, vertical and antidiagonal neighbors.

2, 4, 4, 8, 15, 8, 16, 50, 50, 16, 32, 176, 287, 176, 32, 64, 614, 1725, 1725, 614, 64, 128, 2141, 10299, 18320, 10299, 2141, 128, 256, 7472, 61491, 191025, 191025, 61491, 7472, 256, 512, 26070, 367208, 1994338, 3455416, 1994338, 367208, 26070, 512, 1024

Offset

1,1

Comments

Table starts

...2.....4........8.........16...........32.............64...............128

...4....15.......50........176..........614...........2141..............7472

...8....50......287.......1725........10299..........61491............367208

..16...176.....1725......18320.......191025........1994338..........20834848

..32...614....10299.....191025......3455416.......62640737........1136604611

..64..2141....61491....1994338.....62640737.....1974531630.......62300912853

.128..7472...367208...20834848...1136604611....62300912853.....3418770498783

.256.26070..2192810..217606715..20614698223..1964591851309...187461194033545

.512.90964.13094522.2272854285.373922480489.61959879789835.10281169933978992

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

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

k=3: [order 12]

k=4: [order 19]

k=5: [order 69]

Example

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

Crossrefs

Column 1 is A000079.

Sequence in context: A225982 A282528 A297094 * A181253 A267788 A189696

Adjacent sequences: A283279 A283280 A283281 * A283283 A283284 A283285

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 04 2017

Status

approved