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%I #4 May 17 2018 10:03:54
%S 0,1,1,1,3,1,2,11,11,2,3,10,8,10,3,5,51,21,21,51,5,8,165,46,48,46,165,
%T 8,13,306,103,215,215,103,306,13,21,993,201,798,908,798,201,993,21,34,
%U 2867,512,3055,5232,5232,3055,512,2867,34,55,6818,1123,9810,19701,47440,19701
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0....1....1.....2......3........5.........8..........13...........21
%C ..1....3...11....10.....51......165.......306.........993.........2867
%C ..1...11....8....21.....46......103.......201.........512.........1123
%C ..2...10...21....48....215......798......3055........9810........41744
%C ..3...51...46...215....908.....5232.....19701......135455.......872954
%C ..5..165..103...798...5232....47440....296646.....2733069.....26024851
%C ..8..306..201..3055..19701...296646...3510334....37931518....611105804
%C .13..993..512..9810.135455..2733069..37931518...799135415..19924071081
%C .21.2867.1123.41744.872954.26024851.611105804.19924071081.758781064050
%H R. H. Hardin, <a href="/A304704/b304704.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6
%F k=3: [order 17] for n>20
%F k=4: [order 67] for n>69
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..1..1..1. .0..0..1..0. .0..1..0..0. .0..1..1..0
%e ..1..0..0..0. .0..1..1..0. .1..0..0..0. .0..0..0..1. .0..0..0..0
%e ..0..0..0..0. .1..1..1..1. .0..0..0..1. .1..0..0..0. .0..1..1..0
%e ..1..0..0..1. .0..1..1..0. .1..0..0..1. .0..0..0..1. .0..1..1..0
%e ..0..1..0..0. .0..1..1..1. .0..0..0..0. .0..1..0..0. .0..0..0..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304052.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 17 2018
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