%I #4 Nov 07 2013 18:16:20
%S 3,4,4,7,9,7,12,22,22,12,24,59,96,59,24,48,159,453,453,159,48,103,439,
%T 2302,3572,2302,439,103,222,1236,12052,30269,30269,12052,1236,222,493,
%U 3527,65326,259011,465033,259011,65326,3527,493,1100,10184,358429
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..3 introduced in row major order
%C Table starts
%C ....3.....4........7........12.........24.........48........103..........222
%C ....4.....9.......22........59........159........439.......1236.........3527
%C ....7....22.......96.......453.......2302......12052......65326.......358429
%C ...12....59......453......3572......30269.....259011....2278003.....20081717
%C ...24...159.....2302.....30269.....465033....6871838..105988195...1613424264
%C ...48...439....12052....259011....6871838..169968099.4400551358.111907856129
%C ..103..1236....65326...2278003..105988195.4400551358
%C ..222..3527...358429..20081717.1613424264
%C ..493.10184..1989453.178468093
%C .1100.29679.11087559
%H R. H. Hardin, <a href="/A231343/b231343.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +a(n-4) +3*a(n-5)
%F k=2: a(n) = 5*a(n-1) -6*a(n-2) +2*a(n-3) -8*a(n-4) +6*a(n-5) -a(n-6) +3*a(n-7)
%F k=3: [order 34]
%F k=4: [order 97] for n>98
%e Some solutions for n=4 k=4
%e ..0..0..0..0..0....0..0..0..0..0....0..0..1..1..1....0..1..1..1..1
%e ..1..1..0..0..0....0..0..1..1..1....0..0..1..1..1....0..1..1..1..1
%e ..1..1..2..2..2....0..0..1..1..1....2..2..2..0..0....0..1..1..0..0
%e ..3..3..2..2..2....2..2..2..2..1....2..2..2..0..0....0..2..2..0..0
%e ..3..3..2..2..2....2..2..2..2..1....3..3..3..3..3....0..2..2..2..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 07 2013