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%I #4 Feb 14 2018 07:15:24
%S 0,1,1,1,3,1,2,7,7,2,3,13,15,13,3,5,23,19,19,23,5,8,49,23,40,23,49,8,
%T 13,95,34,85,85,34,95,13,21,177,63,173,179,173,63,177,21,34,359,96,
%U 322,453,453,322,96,359,34,55,705,147,635,1006,1223,1006,635,147,705,55,89,1351
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0...1...1....2....3.....5......8......13......21.......34........55
%C ..1...3...7...13...23....49.....95.....177.....359......705......1351
%C ..1...7..15...19...23....34.....63......96.....147......233.......368
%C ..2..13..19...40...85...173....322.....635....1325.....2806......5877
%C ..3..23..23...85..179...453...1006....2523....6002....14802.....36299
%C ..5..49..34..173..453..1223...3286....9873...28227....86428....253623
%C ..8..95..63..322.1006..3286..13490...49047..183585...713699...2714170
%C .13.177..96..635.2523..9873..49047..231838.1084038..5339757..25938953
%C .21.359.147.1325.6002.28227.183585.1084038.6506278.41165944.255972254
%H R. H. Hardin, <a href="/A299612/b299612.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6
%F k=3: [order 18] for n>19
%F k=4: [order 72] for n>73
%e Some solutions for n=6 k=6
%e ..0..1..1..1..0..1. .0..1..1..0..0..0. .0..1..0..1..0..0. .0..1..0..1..1..0
%e ..0..0..1..1..1..0. .0..0..0..0..0..1. .0..1..0..1..0..1. .0..1..0..0..0..0
%e ..1..1..1..1..1..1. .0..0..0..0..1..0. .1..1..1..1..1..1. .0..1..0..0..0..0
%e ..0..0..1..1..1..1. .1..0..0..0..0..1. .0..0..1..1..1..1. .1..0..0..0..0..1
%e ..1..1..1..0..0..1. .0..1..0..1..0..1. .1..1..1..1..1..0. .1..0..1..0..0..1
%e ..0..0..1..0..1..1. .0..1..0..1..0..0. .0..0..1..1..0..1. .0..1..0..1..0..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297852.
%Y Column 3 is A298050.
%Y Column 4 is A298656.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Feb 14 2018