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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 8
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 (list; table; graph; refs; listen; history; text; internal format)
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 A320908 A248781

Adjacent sequences:  A231541 A231542 A231543 * A231545 A231546 A231547

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 10 2013

STATUS

approved

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Last modified August 21 05:32 EDT 2019. Contains 326162 sequences. (Running on oeis4.)