A231396 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

3, 7, 4, 14, 8, 7, 33, 38, 15, 12, 78, 90, 100, 20, 23, 189, 363, 311, 272, 31, 44, 482, 1163, 1706, 1096, 740, 52, 87, 1225, 3985, 7844, 8340, 4085, 2061, 95, 172, 3238, 14650, 35696, 55788, 41237, 15732, 5834, 180, 343, 8565, 50088, 184692, 345022, 401240

Offset: 1

Author

R. H. Hardin, Nov 08 2013

Keywords

• nonn
• tabl

Comments

Table starts

...3...7.....14......33........78........189........482.......1225.......3238

...4...8.....38......90.......363.......1163.......3985......14650......50088

...7..15....100.....311......1706.......7844......35696.....184692.....873979

..12..20....272....1096......8340......55788.....345022....2502891...16525492

..23..31....740....4085.....41237.....401240....3407422...34218952..319475231

..44..52...2061...15732....217846....3002376...35510853..491895476.6459555901

..87..95...5834...62039...1158551...22654165..374180527.7170248270

.172.180..16521..245850...6261166..172363558.3979476204

.343.351..46969..980361..34110556.1318257485

.684.692.133864.3915982.186830745

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..111

Crossrefs

Column 1 is A023105(n+2)

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) for n>5

k=3: [order 18]

k=4: [order 28] for n>31

Empirical for row n:

n=1: a(n) = 4*a(n-1) +a(n-2) -16*a(n-3) +4*a(n-4) +24*a(n-5) -16*a(n-6)

n=2: [order 21]

n=3: [order 83]