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%I #4 Jan 14 2018 09:01:12
%S 0,0,0,0,1,0,0,1,1,0,0,2,1,2,0,0,3,2,2,3,0,0,5,3,4,3,5,0,0,8,5,6,6,5,
%T 8,0,0,13,8,11,10,11,8,13,0,0,21,13,18,18,18,18,13,21,0,0,34,21,31,32,
%U 62,32,31,21,34,0,0,55,34,53,80,133,133,80,53,34,55,0,0,89,55,91,171,749,624
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0..0..0..0...0....0.....0......0.......0.........0..........0...........0
%C .0..1..1..2...3....5.....8.....13......21........34.........55..........89
%C .0..1..1..2...3....5.....8.....13......21........34.........55..........89
%C .0..2..2..4...6...11....18.....31......53........91........156.........269
%C .0..3..3..6..10...18....32.....80.....171.......528.......1439........4889
%C .0..5..5.11..18...62...133....749....2248.....11243......43303......213698
%C .0..8..8.18..32..133...624...4525...22143....189512....1055639.....8706804
%C .0.13.13.31..80..749..4525..95458..763536..11467153..117226402..1544912726
%C .0.21.21.53.171.2248.22143.763536.6564438.187830170.2268628157.49711027609
%H R. H. Hardin, <a href="/A298167/b298167.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) =
%F k=2: a(n) = a(n-1) +a(n-2)
%F k=3: a(n) = a(n-1) +a(n-2)
%F k=4: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) -2*a(n-5) +a(n-6) +a(n-7)
%F k=5: [order 67]
%e Some solutions for n=8 k=4
%e ..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..1
%e ..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..1
%e ..1..1..0..0. .1..1..1..1. .0..0..1..1. .1..1..0..0. .0..1..0..1
%e ..1..1..0..0. .1..1..1..1. .0..1..0..1. .1..1..0..0. .1..0..1..0
%e ..1..1..0..0. .1..1..1..1. .1..0..1..0. .0..0..1..1. .1..1..0..0
%e ..0..0..1..1. .0..0..0..0. .1..1..0..0. .0..0..1..1. .1..1..0..0
%e ..0..0..1..1. .0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..1..1
%e ..0..0..1..1. .0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..1..1
%Y Column 2 is A000045(n-1).
%Y Column 3 is A000045(n-1).
%K nonn,tabl
%O 1,12
%A _R. H. Hardin_, Jan 14 2018
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