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%I #4 Feb 07 2018 09:52:24
%S 1,2,2,4,8,4,8,26,26,8,16,88,93,88,16,32,298,357,357,298,32,64,1012,
%T 1399,1618,1399,1012,64,128,3440,5513,7667,7667,5513,3440,128,256,
%U 11700,21642,36182,45287,36182,21642,11700,256,512,39804,85000,170056,262230,262230
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 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.....26......88......298......1012.......3440........11700
%C ...4....26.....93.....357.....1399......5513......21642........85000
%C ...8....88....357....1618.....7667.....36182.....170056.......800122
%C ..16...298...1399....7667....45287....262230....1511085......8755520
%C ..32..1012...5513...36182...262230...1870946...13239850.....94146701
%C ..64..3440..21642..170056..1511085..13239850..114730926....998177623
%C .128.11700..85000..800122..8755520..94146701..998177623..10637570858
%C .256.39804.333982.3767186.50742998.670385042.8712117357.113877789805
%H R. H. Hardin, <a href="/A299345/b299345.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) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5)
%F k=3: [order 16] for n>18
%F k=4: [order 64] for n>65
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..1..1..1. .0..0..0..0
%e ..1..1..1..1. .0..0..0..0. .0..0..0..1. .0..1..1..1. .0..0..0..0
%e ..1..1..1..1. .0..0..0..0. .0..0..0..1. .0..1..1..1. .1..1..1..1
%e ..1..1..1..1. .1..1..1..1. .1..1..1..1. .0..1..1..1. .1..1..1..1
%e ..1..1..1..1. .0..0..0..1. .0..1..0..1. .0..1..1..1. .1..1..1..1
%Y Column 1 is A000079(n-1).
%Y Column 2 is A298189.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 07 2018
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