%I #4 Nov 13 2013 10:31:17
%S 1,1,1,3,17,3,8,74,74,8,21,315,854,315,21,55,1343,9892,9892,1343,55,
%T 144,5734,115110,304889,115110,5734,144,377,24495,1339532,9409503,
%U 9409503,1339532,24495,377,987,104655,15587828,290382196,769212993,290382196
%N T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal and vertical 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
%C ....1......17..........74.............315................1343
%C ....3......74.........854............9892..............115110
%C ....8.....315........9892..........304889.............9409503
%C ...21....1343......115110.........9409503...........769212993
%C ...55....5734.....1339532.......290382196.........62871566958
%C ..144...24495....15587828......8961583206.......5138796600020
%C ..377..104655...181392458....276566915938.....420019667031805
%C ..987..447152..2110829288...8535237276423...34330314343879137
%C .2584.1910521.24563317752.263409237229182.2805988700231638418
%H R. H. Hardin, <a href="/A231785/b231785.txt">Table of n, a(n) for n = 1..127</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) = 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 21] for n>22
%F k=4: [order 80] for n>81
%e Some solutions for n=3 k=4
%e ..0..1..1..0....0..0..0..1....0..2..1..0....0..1..2..2....0..0..0..0
%e ..0..0..2..0....0..0..2..1....2..2..1..0....0..0..0..1....2..1..0..1
%e ..1..0..2..2....1..1..1..1....2..0..1..2....2..1..1..1....2..1..0..0
%Y Column 1 is A001906(n-1)
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Nov 13 2013