%I #4 Nov 12 2013 09:34:12

%S 1,1,1,3,5,3,8,25,25,8,21,124,362,124,21,55,599,5110,5110,599,55,144,

%T 2907,69671,193596,69671,2907,144,377,14098,953726,7176194,7176194,

%U 953726,14098,377,987,68345,13036446,266730604,722149510,266730604

%N T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal, vertical, 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 ....1.......5..........25............124.............599.............2907

%C ....3......25.........362...........5110...........69671...........953726

%C ....8.....124........5110.........193596.........7176194........266730604

%C ...21.....599.......69671........7176194.......722149510......72839521581

%C ...55....2907......953726......266730604.....72839521581...19935360619245

%C ..144...14098....13036446.....9902703284...7337927223290.5448852806527104

%C ..377...68345...178192422...367678630271.739300928401336

%C ..987..331411..2435768976.13651615789060

%C .2584.1606976.33294651915

%H R. H. Hardin, <a href="/A231641/b231641.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) for n>3

%F k=2: a(n) = 7*a(n-1) -11*a(n-2) +4*a(n-3) -14*a(n-4) +48*a(n-5) -48*a(n-6) +16*a(n-7)

%F k=3: [order 38] for n>39

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A001906(n-1)

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Nov 12 2013