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A301784 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

%I A301784 #4 Mar 26 2018 16:28:31
%S A301784 1,2,2,4,8,4,8,32,32,8,16,128,240,128,16,32,512,1808,1808,512,32,64,
%T A301784 2048,13616,25872,13616,2048,64,128,8192,102544,369936,369936,102544,
%U A301784 8192,128,256,32768,772272,5289488,10033408,5289488,772272,32768,256,512,131072
%N A301784 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.
%C A301784 Table starts
%C A301784 ...1......2........4...........8............16...............32
%C A301784 ...2......8.......32.........128...........512.............2048
%C A301784 ...4.....32......240........1808.........13616...........102544
%C A301784 ...8....128.....1808.......25872........369936..........5289488
%C A301784 ..16....512....13616......369936......10033408........272151040
%C A301784 ..32...2048...102544.....5289488.....272151040......14004742144
%C A301784 ..64...8192...772272....75632400....7381982784.....720677122368
%C A301784 .128..32768..5816080..1081436176..200232929792...37085631944448
%C A301784 .256.131072.43801648.15463010576.5431228387584.1908405940870656
%H A301784 R. H. Hardin, <a href="/A301784/b301784.txt">Table of n, a(n) for n = 1..364</a>
%F A301784 Empirical for column k:
%F A301784 k=1: a(n) = 2*a(n-1)
%F A301784 k=2: a(n) = 4*a(n-1)
%F A301784 k=3: a(n) = 7*a(n-1) +4*a(n-2)
%F A301784 k=4: a(n) = 13*a(n-1) +20*a(n-2) -16*a(n-3) -64*a(n-4)
%F A301784 k=5: [order 8]
%F A301784 k=6: [order 20]
%F A301784 k=7: [order 46]
%e A301784 Some solutions for n=5 k=4
%e A301784 ..0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..0
%e A301784 ..0..1..0..1. .1..0..0..1. .0..1..1..1. .0..1..0..0. .0..0..1..1
%e A301784 ..0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..0..1. .0..1..1..1
%e A301784 ..1..0..1..1. .1..0..1..0. .1..0..0..1. .1..1..1..1. .0..1..0..0
%e A301784 ..0..0..0..0. .1..1..1..0. .1..1..1..0. .1..0..1..0. .0..0..0..1
%Y A301784 Column 1 is A000079(n-1).
%Y A301784 Column 2 is A004171(n-1).
%K A301784 nonn,tabl
%O A301784 1,2
%A A301784 _R. H. Hardin_, Mar 26 2018