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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A023105(n+2)

Sequence in context: A272668 A014406 A154426 * A231343 A121924 A241740

Adjacent sequences: A231216 A231217 A231218 * A231220 A231221 A231222

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 05 2013

Status

approved