A280480 T(n,k)=Number of nXk 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 0, 0, 6, 0, 6, 22, 30, 0, 6, 63, 208, 158, 0, 30, 162, 997, 1939, 846, 0, 54, 381, 4070, 15104, 17406, 4446, 0, 158, 884, 15441, 100306, 214635, 149057, 22734, 0, 342, 1995, 55149, 618883, 2272190, 2886700, 1224092, 113310, 0, 846, 4478, 189470, 3589912

Offset

1,5

Comments

Table starts

.0.......1.........0...........6............6...........30...........54

.0.......6........22..........63..........162..........381..........884

.0......30.......208.........997.........4070........15441........55149

.0.....158......1939.......15104.......100306.......618883......3589912

.0.....846.....17406......214635......2272190.....22475478....208736159

.0....4446....149057.....2886700.....48481917....767741328..11437392975

.0...22734...1224092....37224679....990070284..25082093017.599110195185

.0..113310...9717407...464804972..19550495121.792009247239

.0..552654..75078490..5658641517.375972018492

.0.2647390.567486429.67497024458

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

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

k=2: a(n) = 15*a(n-1) -87*a(n-2) +245*a(n-3) -348*a(n-4) +240*a(n-5) -64*a(n-6)

k=3: [order 9] for n>10

k=4: [order 21] for n>22

k=5: [order 38] for n>39

Empirical for row n:

n=1: a(n) = 3*a(n-1) +3*a(n-2) -11*a(n-3) -6*a(n-4) +12*a(n-5) +8*a(n-6)

n=2: [order 8] for n>10

n=3: [order 26] for n>32

Example

Some solutions for n=4 k=4
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..1. .0..0..1..1
..1..1..0..0. .0..1..1..1. .1..1..0..0. .2..2..1..1. .1..1..0..0
..0..0..1..2. .0..1..1..2. .1..0..2..2. .2..2..2..2. .0..0..0..0
..1..1..2..2. .1..2..2..2. .2..2..1..1. .2..1..1..1. .2..0..0..0

Crossrefs

Row 1 is A279865.

Sequence in context: A223033 A237444 A222918 * A223104 A222722 A222747

Adjacent sequences: A280477 A280478 A280479 * A280481 A280482 A280483

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 04 2017

Status

approved