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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order
12

%I #4 Nov 09 2013 07:29:38

%S 3,7,4,14,8,7,33,38,15,12,78,90,100,20,24,197,363,311,272,32,48,531,

%T 1163,1709,1096,741,56,103,1471,4151,7973,8426,4138,2093,111,222,4350,

%U 16054,37494,57426,42229,16384,6036,230,493,13011,57977,207123,367803,425678

%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, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order

%C Table starts

%C ....3....7.....14......33.......78.......197.......531......1471.......4350

%C ....4....8.....38......90......363......1163......4151.....16054......57977

%C ....7...15....100.....311.....1709......7973.....37494....207123....1039577

%C ...12...20....272....1096.....8426.....57426....367803...2845485...20018093

%C ...24...32....741....4138....42229....425678...3759661..40527272..407446601

%C ...48...56...2093...16384...229889...3306466..41018349.609662051.8698312947

%C ..103..111...6036...67189..1275119..26262415.459675854

%C ..222..230..17569..280852..7279729.212142656

%C ..493..501..51839.1195147.42382102

%C .1100.1108.154480.5145988

%H R. H. Hardin, <a href="/A231463/b231463.txt">Table of n, a(n) for n = 1..97</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) = 3*a(n-1) +a(n-2) -7*a(n-3) +a(n-4) +3*a(n-5) for n>7

%F k=3: [order 32]

%F k=4: [order 52] for n>55

%F Empirical for row n:

%F n=1: [order 10]

%F n=2: [order 41]

%e Some solutions for n=5 k=4

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

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

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

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

%e ..1..1..1..0..0....2..2..2..3..3....1..1..0..0..0....2..2..2..3..3

%e ..1..1..0..0..0....3..3..3..3..3....0..0..1..1..1....2..2..3..3..3

%Y Column 1 is A231337

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 09 2013