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%I #4 May 11 2018 14:16:56
%S 1,2,2,4,4,4,8,14,14,8,16,28,27,28,16,32,94,71,71,94,32,64,284,225,
%T 290,225,284,64,128,752,613,1266,1266,613,752,128,256,2244,1752,4733,
%U 6373,4733,1752,2244,256,512,6532,5102,18855,27505,27505,18855,5102,6532,512
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2.....4......8......16.......32........64........128.........256
%C ...2....4....14.....28......94......284.......752.......2244........6532
%C ...4...14....27.....71.....225......613......1752.......5102.......14673
%C ...8...28....71....290....1266.....4733.....18855......76887......308978
%C ..16...94...225...1266....6373....27505....127511.....633229.....3052998
%C ..32..284...613...4733...27505...135445....741942....4355191....24554331
%C ..64..752..1752..18855..127511...741942...4921043...36193582...250785575
%C .128.2244..5102..76887..633229..4355191..36193582..343449680..2937754820
%C .256.6532.14673.308978.3052998.24554331.250785575.2937754820.30008468246
%H R. H. Hardin, <a href="/A304347/b304347.txt">Table of n, a(n) for n = 1..219</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6
%F k=3: [order 15] for n>16
%F k=4: [order 57] for n>60
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..1..0..1
%e ..1..0..0..1. .1..0..1..1. .0..0..1..1. .0..1..0..1. .0..0..1..1
%e ..0..0..0..0. .0..1..1..1. .1..1..1..1. .1..0..1..0. .1..0..1..0
%e ..1..0..0..1. .1..1..1..0. .0..0..0..0. .0..0..1..1. .0..1..0..1
%e ..1..0..0..0. .1..1..1..0. .1..1..0..0. .0..1..0..1. .0..0..1..1
%Y Column 1 is A000079(n-1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, May 11 2018
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