A231219 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.

3, 4, 4, 7, 9, 7, 12, 22, 22, 12, 23, 59, 93, 59, 23, 44, 156, 408, 408, 156, 44, 87, 413, 1793, 2892, 1793, 413, 87, 172, 1098, 7844, 20027, 20027, 7844, 1098, 172, 343, 2919, 34609, 139438, 226764, 139438, 34609, 2919, 343, 684, 7760, 152421, 969461

Offset: 1

Author

R. H. Hardin, Nov 05 2013

Keywords

• nonn
• tabl

Comments

Table starts

...3.....4.......7........12..........23............44.............87

...4.....9......22........59.........156...........413...........1098

...7....22......93.......408........1793..........7844..........34609

..12....59.....408......2892.......20027........139438.........969461

..23...156....1793.....20027......226764.......2534951.......28439115

..44...413....7844....139438.....2534951......45593903......820418528

..87..1098...34609....969461....28439115.....820418528....23748656906

.172..2919..152421...6745110...318236849...14743946094...685733582035

.343..7760..672446..46938804..3565691309..265057746273.19812622781057

.684.20633.2965705.326645650.39935313475.4764850607558

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..127

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) = 3*a(n-1) -a(n-2) +a(n-3) -2*a(n-4)

k=3: [order 19]

k=4: [order 68]