A231544 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, vertical and antidiagonal neighbors

2, 2, 2, 4, 6, 4, 7, 20, 20, 7, 12, 57, 116, 57, 12, 21, 164, 589, 589, 164, 21, 37, 485, 3001, 5235, 3001, 485, 37, 65, 1424, 15644, 46122, 46122, 15644, 1424, 65, 114, 4169, 81179, 417298, 698721, 417298, 81179, 4169, 114, 200, 12228, 420243, 3763223, 10928292

Offset

1,1

Comments

Table starts

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

...2.....6.......20.........57..........164.............485..............1424

...4....20......116........589.........3001...........15644.............81179

...7....57......589.......5235........46122..........417298...........3763223

..12...164.....3001......46122.......698721........10928292.........170393737

..21...485....15644.....417298.....10928292.......296647240........8028429092

..37..1424....81179....3763223....170393737......8028429092......377320795091

..65..4169...420243...33812753...2643967833....216093538039....17623244476340

.114.12228..2177937..304137386..41079980720...5824887373442...824325064919737

.200.35868.11287977.2736503160.638622184605.157116139854017.38588079925163243

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4

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

k=3: [order 22]

k=4: [order 61]

Example

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

Crossrefs

Column 1 is A005251(n+2)

Sequence in context: A240433 A217637 A231515 * A086420 A328106 A342336

Adjacent sequences: A231541 A231542 A231543 * A231545 A231546 A231547

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 10 2013

Status

approved