%I #4 Mar 13 2018 07:45:44
%S 1,2,2,4,8,4,8,32,32,8,16,128,228,128,16,32,512,1672,1672,512,32,64,
%T 2048,12228,23096,12228,2048,64,128,8192,89472,317504,317504,89472,
%U 8192,128,256,32768,654628,4369224,8170504,4369224,654628,32768,256,512,131072
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1......2........4...........8............16...............32
%C ...2......8.......32.........128...........512.............2048
%C ...4.....32......228........1672.........12228............89472
%C ...8....128.....1672.......23096........317504..........4369224
%C ..16....512....12228......317504.......8170504........210678360
%C ..32...2048....89472.....4369224.....210678360......10189867088
%C ..64...8192...654628....60123512....5431609016.....492720806016
%C .128..32768..4789672...827349312..140040313680...23826737802264
%C .256.131072.35044228.11385017480.3610578476036.1152195114983576
%H R. H. Hardin, <a href="/A300804/b300804.txt">Table of n, a(n) for n = 1..312</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 4*a(n-1)
%F k=3: a(n) = 7*a(n-1) +3*a(n-2) -5*a(n-3)
%F k=4: [order 11]
%F k=5: [order 27] for n>29
%F k=6: [order 85] for n>87
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..0..1..0. .0..0..0..0. .0..0..0..0. .0..0..1..0
%e ..1..0..1..1. .0..0..0..1. .1..1..0..0. .1..0..0..1. .0..1..1..0
%e ..1..0..0..1. .1..1..0..1. .1..1..1..0. .1..1..0..1. .1..0..0..1
%e ..0..0..1..1. .1..0..0..0. .0..0..1..0. .1..0..0..1. .1..1..0..0
%e ..1..0..1..1. .0..1..0..1. .0..0..1..1. .1..0..1..1. .0..0..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A004171(n-1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 13 2018