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%I #4 Feb 19 2018 15:32:18
%S 1,2,2,4,7,4,8,13,13,8,16,29,20,29,16,32,73,44,44,73,32,64,157,123,
%T 174,123,157,64,128,353,343,1059,1059,343,353,128,256,869,973,4543,
%U 7013,4543,973,869,256,512,1993,2774,19006,40015,40015,19006,2774,1993,512,1024
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6 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....7...13.....29.......73.......157.........353..........869
%C ...4...13...20.....44......123.......343.........973.........2774
%C ...8...29...44....174.....1059......4543.......19006........90935
%C ..16...73..123...1059.....7013.....40015......265422......1763437
%C ..32..157..343...4543....40015....388453.....3956148.....40566160
%C ..64..353..973..19006...265422...3956148....61726046....969500658
%C .128..869.2774..90935..1763437..40566160...969500658..23457257837
%C .256.1993.7993.415860.11422152.419678087.15429018063.574690229422
%H R. H. Hardin, <a href="/A299806/b299806.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6
%F k=3: [order 16] for n>17
%F k=4: [order 66] for n>70
%e Some solutions for n=5 k=4
%e ..0..1..1..1. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
%e ..0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..1
%e ..0..0..0..1. .0..0..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..1
%e ..0..0..0..1. .0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..1
%e ..0..1..1..0. .0..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A298215.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 19 2018
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