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%I #4 Mar 31 2014 07:46:23
%S 2,2,2,4,2,4,4,6,6,4,8,4,16,4,8,8,10,16,16,10,8,16,8,42,18,42,8,16,16,
%T 20,44,52,52,44,20,16,32,16,114,62,154,62,114,16,32,32,40,122,162,178,
%U 178,162,122,40,32,64,32,314,204,494,282,494,204,314,32,64,64,80,340,530,600
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest, modulo 3
%C Table starts
%C ..2..2...4...4....8....8....16....16....32.....32.....64.....64.....128.....128
%C ..2..2...6...4...10....8....20....16....40.....32.....80.....64.....160.....128
%C ..4..6..16..16...42...44...114...122...314....340....872....950....2432....2658
%C ..4..4..16..18...52...62...162...204...530....672...1736...2198....5706....7202
%C ..8.10..42..52..154..178...494...600..1606...2014...5262...6690...17464...22360
%C ..8..8..44..62..178..282...710..1074..2770...4162..10836..15764...41374...59680
%C .16.20.114.162..494..710..1976..2884..7958..12074..31824..49078..130758..197208
%C .16.16.122.204..600.1074..2884..5706.14686..25224..66774.113794..307698..508002
%C .32.40.314.530.1606.2770..7958.14686.42470..72446.200916.360716..984770.1730698
%C .32.32.340.672.2014.4162.12074.25224.72446.147092.407954.778294.2194512.4046228
%H R. H. Hardin, <a href="/A240039/b240039.txt">Table of n, a(n) for n = 1..511</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-2)
%F k=2: a(n) = 2*a(n-2) for n>5
%F k=3: a(n) = 4*a(n-2) -3*a(n-4) -a(n-6) for n>7
%F k=4: [order 24] for n>27
%F k=5: [order 86] for n>89
%e Some solutions for n=3 k=4
%e ..2..1..1..2....2..1..2..1....2..1..2..1....1..2..1..2....1..2..1..2
%e ..1..0..0..0....1..0..0..0....1..0..0..0....2..0..0..0....2..0..0..0
%e ..1..0..0..0....1..0..0..0....2..0..0..0....2..0..0..0....2..0..0..1
%Y Column 1 is A016116(n+1)
%Y Column 2 is A163888(n-2) for n>3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Mar 31 2014
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