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%I #4 Jun 27 2018 15:35:00
%S 1,2,2,3,5,3,5,9,9,5,8,21,14,21,8,13,57,29,29,57,13,21,125,71,105,71,
%T 125,21,34,289,153,365,365,153,289,34,55,741,358,1135,1867,1135,358,
%U 741,55,89,1737,956,4802,6518,6518,4802,956,1737,89,144,4045,2612,21363,41303
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..1....2....3.....5.......8.......13.........21...........34............55
%C ..2....5....9....21......57......125........289..........741..........1737
%C ..3....9...14....29......71......153........358..........956..........2612
%C ..5...21...29...105.....365.....1135.......4802........21363.........89321
%C ..8...57...71...365....1867.....6518......41303.......312366.......1912290
%C .13..125..153..1135....6518....42075.....496125......5256306......54317972
%C .21..289..358..4802...41303...496125...10057887....174856739....2842217588
%C .34..741..956.21363..312366..5256306..174856739...5109468434..127247367597
%C .55.1737.2612.89321.1912290.54317972.2842217588.127247367597.4994868880193
%H R. H. Hardin, <a href="/A316239/b316239.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) = 2*a(n-1) -a(n-2) +8*a(n-3) -8*a(n-4)
%F k=3: [order 18] for n>20
%F k=4: [order 64] for n>67
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..1..0..1
%e ..1..0..0..0. .0..0..0..1. .1..0..1..0. .1..0..1..0. .1..1..0..0
%e ..0..1..1..1. .1..0..0..0. .1..0..1..1. .1..1..0..0. .0..0..1..1
%e ..1..1..1..0. .0..1..1..1. .0..1..0..0. .1..1..0..0. .1..1..0..0
%e ..1..1..1..1. .1..1..1..0. .1..1..0..1. .0..1..0..1. .0..1..0..1
%Y Column 1 is A000045(n+1).
%Y Column 2 is A304349.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jun 27 2018
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