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%I #4 Jan 07 2017 08:07:44
%S 1,2,2,4,11,5,11,59,82,14,30,338,858,612,41,82,1917,10205,12484,4568,
%T 122,224,10893,119440,310365,181640,34096,365,612,61880,1401470,
%U 7533245,9439606,2642832,254496,1094,1672,351541,16438612,183331502,474736149
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
%C Table starts
%C ....1.........2............4..............11...............30................82
%C ....2........11...........59.............338.............1917.............10893
%C ....5........82..........858...........10205...........119440...........1401470
%C ...14.......612........12484..........310365..........7533245.........183331502
%C ...41......4568.......181640.........9439606........474736149.......23952262535
%C ..122.....34096......2642832.......287101721......29920114246.....3130289979912
%C ..365....254496.....38452768......8732086113....1885698283255...409089889172506
%C .1094...1899584....559481408....265582964074..118845116023725.53463025958093933
%C .3281..14178688...8140361856...8077601392565.7490149091439288
%C .9842.105831168.118440917248.245677069239189
%H R. H. Hardin, <a href="/A280673/b280673.txt">Table of n, a(n) for n = 1..97</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -3*a(n-2)
%F k=2: a(n) = 8*a(n-1) -4*a(n-2) for n>3
%F k=3: a(n) = 14*a(n-1) +8*a(n-2)
%F k=4: a(n) = 29*a(n-1) +44*a(n-2) -27*a(n-3) -81*a(n-4) for n>5
%F k=5: [order 8] for n>9
%F k=6: [order 20] for n>22
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
%F n=2: a(n) = 5*a(n-1) +6*a(n-2) -11*a(n-3) -7*a(n-4) +4*a(n-5) for n>6
%F n=3: [order 18] for n>20
%F n=4: [order 73] for n>78
%e Some solutions for n=3 k=4
%e ..0..1..0..0. .0..1..0..2. .0..1..0..1. .0..0..1..0. .0..1..1..0
%e ..0..1..2..1. .2..0..2..1. .0..2..1..0. .2..2..1..1. .2..0..2..0
%e ..1..2..0..0. .2..1..0..2. .2..0..2..0. .1..0..2..2. .1..0..1..1
%Y Column 1 is A007051(n-1).
%Y Column 2 is A209094.
%Y Row 1 is A021006(n-3).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 07 2017
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