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%I #4 Jul 14 2018 15:00:27
%S 1,2,2,4,8,4,8,32,32,8,16,128,247,128,16,32,512,1905,1905,512,32,64,
%T 2048,14711,28248,14711,2048,64,128,8192,113606,420345,420345,113606,
%U 8192,128,256,32768,877309,6256258,12075849,6256258,877309,32768,256,512,131072
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5 or 6 king-move 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......247........1905.........14711...........113606
%C ...8....128.....1905.......28248........420345..........6256258
%C ..16....512....14711......420345......12075849........347046960
%C ..32...2048...113606.....6256258.....347046960......19261290694
%C ..64...8192...877309....93109949....9972851339....1068884675914
%C .128..32768..6774916..1385723098..286582122564...59316329979368
%C .256.131072.52318510.20623265507.8235306627639.3291689981719718
%H R. H. Hardin, <a href="/A316808/b316808.txt">Table of n, a(n) for n = 1..220</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) = 8*a(n-1) -3*a(n-2) +7*a(n-3) -3*a(n-4)
%F k=4: a(n) = 15*a(n-1) -5*a(n-2) +50*a(n-3) -18*a(n-4) -81*a(n-5) +4*a(n-6) +20*a(n-7)
%F k=5: [order 22]
%F k=6: [order 59]
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..0..1. .0..0..0..1. .0..0..1..0. .0..0..0..1
%e ..0..0..0..0. .0..1..1..1. .0..0..1..0. .0..0..0..0. .1..0..0..0
%e ..0..1..1..1. .1..1..0..1. .1..1..0..1. .1..0..0..1. .1..0..1..1
%e ..0..0..1..0. .1..0..0..0. .0..1..1..0. .0..1..1..1. .0..0..1..0
%e ..1..0..1..0. .1..1..0..1. .0..0..0..1. .1..0..1..0. .0..1..0..1
%Y Column 1 is A000079(n-1).
%Y Column 2 is A004171(n-1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jul 14 2018
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