%I #4 Nov 08 2013 08:29:19
%S 1,2,2,4,5,4,12,16,16,12,33,51,69,51,33,102,180,314,314,180,102,329,
%T 685,1588,2190,1588,685,329,1075,2735,8664,15384,15384,8664,2735,1075,
%U 3622,11243,48485,115303,151357,115303,48485,11243,3622,12298,47120,278067
%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, vertical and antidiagonal neighbors, with values 0..3 introduced in row major order
%C Table starts
%C .....1......2.......4........12..........33...........102............329
%C .....2......5......16........51.........180...........685...........2735
%C .....4.....16......69.......314........1588..........8664..........48485
%C ....12.....51.....314......2190.......15384........115303.........875548
%C ....33....180....1588.....15384......151357.......1570792.......16473680
%C ...102....685....8664....115303.....1570792......22223936......323672993
%C ...329...2735...48485....875548....16473680.....323672993.....6484084119
%C ..1075..11243..278067...6891052...177642195....4805725804...132637022443
%C ..3622..47120.1614600..54253511..1920518549...71571627525..2720040353857
%C .12298.199945.9457286.432215971.20952334810.1071735830464.56182108648915
%H R. H. Hardin, <a href="/A231363/b231363.txt">Table of n, a(n) for n = 1..143</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) +5*a(n-2) -5*a(n-3) -24*a(n-4) -2*a(n-5) +15*a(n-6) +9*a(n-7)
%F k=2: [order 13] for n>14
%F k=3: [order 29] for n>31
%F k=4: [order 79] for n>83
%e Some solutions for n=4 k=4
%e ..0..0..1..2..2....0..0..1..2..2....0..0..1..1..1....0..0..1..1..2
%e ..0..1..1..2..2....0..1..1..2..3....0..0..1..1..1....0..1..1..2..2
%e ..1..1..3..3..2....1..1..2..3..3....0..1..1..1..1....1..1..1..2..3
%e ..3..3..3..3..2....1..2..2..3..3....1..1..1..1..2....1..1..2..3..3
%e ..3..3..3..2..2....2..2..2..3..3....1..1..1..2..2....1..2..2..3..3
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Nov 08 2013