A231441 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order

1, 2, 2, 3, 4, 3, 6, 8, 8, 6, 11, 17, 21, 17, 11, 23, 45, 54, 54, 45, 23, 47, 104, 185, 182, 185, 104, 47, 102, 280, 561, 820, 820, 561, 280, 102, 221, 752, 1943, 3071, 4450, 3071, 1943, 752, 221, 492, 2076, 6756, 13458, 21472, 21472, 13458, 6756, 2076, 492, 1099, 5947

Offset

1,2

Comments

Table starts

...1....2.....3.......6.......11.......23.......47......102.......221.......492

...2....4.....8......17.......45......104......280......752......2076......5947

...3....8....21......54......185......561.....1943.....6756.....24003.....88488

...6...17....54.....182......820.....3071....13458....59480....266481...1252868

..11...45...185.....820.....4450....21472...117959...653280...3702873..21843997

..23..104...561....3071....21472...133646...919000..6530487..46899990.351910410

..47..280..1943...13458...117959...919000..7859324.70278737.631712523

.102..752..6756...59480...653280..6530487.70278737

.221.2076.24003..266481..3702873.46899990

.492.5947.88488.1252868.21843997

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

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

k=2: [order 19]

k=3: [order 24]

Example

Some solutions for n=5 k=4
..0..0..0..1..1..1....0..0..0..0..0..0....0..0..1..1..1..1....0..0..0..0..0..0
..0..0..0..1..1..1....0..0..0..0..0..0....0..0..1..1..1..1....0..0..0..0..0..0
..0..0..2..2..1..1....1..1..0..0..1..1....0..0..0..1..1..1....0..0..0..0..0..0
..2..2..2..2..2..2....1..1..1..1..1..1....0..0..0..1..1..1....1..1..1..1..1..1
..2..2..3..3..2..2....2..2..1..1..3..3....2..2..0..0..1..1....1..1..1..1..1..1
..3..3..3..3..3..3....2..2..2..3..3..3....2..2..2..0..0..0....0..0..1..1..0..0
..3..3..3..3..3..3....2..2..2..3..3..3....2..2..2..0..0..0....0..0..0..0..0..0

Crossrefs

Column 1 is A199142(n+2)

Sequence in context: A360999 A343299 A231227 * A284199 A284165 A284113

Adjacent sequences: A231438 A231439 A231440 * A231442 A231443 A231444

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 09 2013

Status

approved