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%I #4 Jul 24 2018 10:32:30
%S 1,2,2,4,8,4,8,21,21,8,16,49,46,49,16,32,120,150,150,120,32,64,293,
%T 488,490,488,293,64,128,719,1468,2306,2306,1468,719,128,256,1774,4626,
%U 7988,17039,7988,4626,1774,256,512,4389,14720,29512,101712,101712,29512,14720
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2.....4......8.......16........32..........64..........128
%C ...2....8....21.....49......120.......293.........719.........1774
%C ...4...21....46....150......488......1468........4626........14720
%C ...8...49...150....490.....2306......7988.......29512.......118116
%C ..16..120...488...2306....17039....101712......575421......3632635
%C ..32..293..1468...7988...101712....929233.....7953354.....80002584
%C ..64..719..4626..29512...575421...7953354....98315821...1489532375
%C .128.1774.14720.118116..3632635..80002584..1489532375..35202633059
%C .256.4389.45811.442877.22324637.773208574.21712800613.807772568098
%H R. H. Hardin, <a href="/A317230/b317230.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) = 3*a(n-1) +a(n-2) -4*a(n-3) -4*a(n-4) for n>5
%F k=3: [order 10] for n>12
%F k=4: [order 21] for n>25
%F k=5: [order 84] for n>88
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..0..0..1. .0..1..0..0. .0..0..1..1. .0..1..1..0
%e ..1..1..1..1. .0..0..0..0. .1..1..0..0. .0..0..0..1. .1..1..1..1
%e ..1..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..1..1
%e ..1..1..1..1. .0..0..1..0. .0..0..1..1. .1..1..0..0. .0..0..1..1
%e ..0..1..1..1. .1..0..0..0. .0..0..1..0. .1..0..0..0. .0..0..0..1
%Y Column 1 is A000079(n-1).
%Y Column 2 is A303721.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jul 24 2018
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