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%I #6 Jan 16 2018 11:27:40
%S 1,2,2,4,7,4,8,13,13,8,16,29,20,29,16,32,69,26,26,69,32,64,137,43,46,
%T 43,137,64,128,301,72,130,130,72,301,128,256,705,115,233,308,233,115,
%U 705,256,512,1461,189,448,515,515,448,189,1461,512,1024,3193,318,877,1084
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2...4....8...16...32....64...128....256....512....1024....2048....4096
%C ...2....7..13...29...69..137...301...705...1461...3193....7373...15729...34405
%C ...4...13..20...26...43...72...115...189....318....526.....874....1473....2482
%C ...8...29..26...46..130..233...448...877...1605...3284....6774...13516...26780
%C ..16...69..43..130..308..515..1084..2374...4754..10042...21207...44405...93926
%C ..32..137..72..233..515..990..1798..4079...9026..18246...39612...86150..184768
%C ..64..301.115..448.1084.1798..4679.10688..22503..53875..123435..278930..642076
%C .128..705.189..877.2374.4079.10688.26963..60768.151924..370070..871422.2153007
%C .256.1461.318.1605.4754.9026.22503.60768.153319.389464.1009970.2538759.6516314
%H R. H. Hardin, <a href="/A298294/b298294.txt">Table of n, a(n) for n = 1..287</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) -2*a(n-2) +8*a(n-3) -20*a(n-4) +8*a(n-5) for n>6
%F k=3: [order 17] for n>19
%F k=4: [order 67] for n>70
%e Some solutions for n=7 k=4
%e ..0..1..0..1. .0..0..0..1. .0..1..1..0. .0..0..1..0. .0..0..1..0
%e ..0..0..0..1. .1..1..1..0. .0..0..1..0. .1..1..1..0. .1..0..1..0
%e ..0..0..1..0. .0..1..1..0. .1..1..1..0. .0..1..0..1. .0..0..1..0
%e ..1..0..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..1. .1..1..1..1
%e ..0..0..0..0. .1..0..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..0
%e ..1..1..1..1. .1..0..1..1. .1..1..1..0. .1..0..0..0. .0..1..0..1
%e ..0..0..0..0. .1..0..1..0. .0..0..1..0. .1..0..1..1. .0..1..0..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A297883.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 16 2018
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