%I #4 Jul 03 2018 09:21:32
%S 0,1,1,1,3,1,2,11,11,2,3,10,9,10,3,5,51,23,23,51,5,8,165,58,48,58,165,
%T 8,13,306,126,229,229,126,306,13,21,993,272,850,1591,850,272,993,21,
%U 34,2867,672,3223,6590,6590,3223,672,2867,34,55,6818,1553,10880,29406,53863
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5, 6 or 8 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....9....23......58......126.......272.........672.........1553
%C ..2...10...23....48.....229......850......3223.......10880........45692
%C ..3...51...58...229....1591.....6590.....29406......180787......1110885
%C ..5..165..126...850....6590....53863....349456.....3164734.....29901503
%C ..8..306..272..3223...29406...349456...4145337....44700278....711845805
%C .13..993..672.10880..180787..3164734..44700278...935229204..23033473439
%C .21.2867.1553.45692.1110885.29901503.711845805.23033473439.873192441329
%H R. H. Hardin, <a href="/A316455/b316455.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..0..0. .0..0..0..0. .0..1..1..0. .0..0..0..0. .0..0..0..1
%e ..1..0..0..1. .1..0..1..0. .0..0..0..0. .0..1..0..1. .1..0..0..1
%e ..1..0..0..1. .0..0..0..0. .0..1..1..0. .0..0..0..0. .0..0..1..1
%e ..1..1..1..1. .1..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..0
%e ..1..0..0..1. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..1..1..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304052.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jul 03 2018
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