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%I #4 Nov 15 2013 07:25:41
%S 1,1,3,3,17,9,8,137,74,27,21,948,1740,315,81,55,6975,31167,22759,1343,
%T 243,144,50323,614818,1082472,297099,5734,729,377,366170,11900005,
%U 57946241,37368831,3882566,24495,2187,987,2657785,232002949,3045772177
%N T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions)
%C Table starts
%C ....1......1.........3.............8...............21...................55
%C ....3.....17.......137...........948.............6975................50323
%C ....9.....74......1740.........31167...........614818.............11900005
%C ...27....315.....22759.......1082472.........57946241...........3045772177
%C ...81...1343....297099......37368831.......5429359691.........773715251151
%C ..243...5734...3882566....1291573433.....509273459716......196795864115357
%C ..729..24495..50739125...44640322903...47773200503463....50062652312668838
%C .2187.104655.663117735.1542901809201.4481443113541663.12735271817562619233
%H R. H. Hardin, <a href="/A231908/b231908.txt">Table of n, a(n) for n = 1..96</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1)
%F k=2: a(n) = 6*a(n-1) -8*a(n-2) +2*a(n-3) +3*a(n-4) -a(n-5) for n>6
%F k=3: [order 17] for n>18
%F k=4: [order 81] for n>82
%F Empirical for row n:
%F n=1: a(n) = 3*a(n-1) -a(n-2) for n>3
%F n=2: a(n) = 9*a(n-1) -5*a(n-2) -66*a(n-3) +78*a(n-4) +4*a(n-5) -16*a(n-6)
%F n=3: [order 37] for n>38
%e Some solutions for n=3 k=4
%e ..0..0..2..1....0..0..0..1....0..2..0..1....0..2..2..1....0..0..0..0
%e ..1..0..1..1....2..1..0..0....2..2..2..0....2..2..1..2....0..0..1..0
%e ..0..2..0..0....1..2..2..1....2..0..0..2....2..0..0..1....1..1..0..2
%Y Column 1 is A000244(n-1)
%Y Column 2 is A231779
%Y Row 1 is A001906(n-1)
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Nov 15 2013
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