A231219 - OEIS

%I #4 Nov 05 2013 16:32:51

%S 3,4,4,7,9,7,12,22,22,12,23,59,93,59,23,44,156,408,408,156,44,87,413,

%T 1793,2892,1793,413,87,172,1098,7844,20027,20027,7844,1098,172,343,

%U 2919,34609,139438,226764,139438,34609,2919,343,684,7760,152421,969461

%N 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

%C Table starts

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

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

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

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

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

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

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

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

%C .343..7760..672446..46938804..3565691309..265057746273.19812622781057

%C .684.20633.2965705.326645650.39935313475.4764850607558

%H R. H. Hardin, <a href="/A231219/b231219.txt">Table of n, a(n) for n = 1..127</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) -a(n-2) +a(n-3) -2*a(n-4)

%F k=3: [order 19]

%F k=4: [order 68]

%e Some solutions for n=4 k=4

%e ..0..0..0..1..1....0..0..0..0..0....0..0..0..0..0....0..0..1..1..0

%e ..0..0..0..1..1....1..1..1..1..1....1..1..1..2..2....0..0..1..1..0

%e ..0..0..0..2..2....1..0..0..0..1....1..1..1..2..2....0..0..1..1..0

%e ..0..0..0..2..2....1..0..0..0..1....1..1..1..2..2....0..0..1..1..0

%e ..2..2..2..2..2....1..1..1..1..1....1..1..1..2..2....0..0..1..1..0

%Y Column 1 is A023105(n+2)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 05 2013