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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
8
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 05 2013
STATUS
approved