%I #4 May 19 2018 12:25:51
%S 1,2,2,4,4,4,8,12,12,8,16,24,25,24,16,32,64,51,51,64,32,64,184,165,
%T 132,165,184,64,128,432,419,502,502,419,432,128,256,1088,1009,1638,
%U 3009,1638,1009,1088,256,512,2944,2697,4816,12763,12763,4816,2697,2944,512,1024
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2....4.....8.....16......32.......64.......128.........256..........512
%C ...2....4...12....24.....64.....184......432......1088........2944.........7360
%C ...4...12...25....51....165.....419.....1009......2697........7091........18147
%C ...8...24...51...132....502....1638.....4816.....15697.......51711.......162366
%C ..16...64..165...502...3009...12763....45988....205950......912997......3690448
%C ..32..184..419..1638..12763...67025...294924...1719748.....9770201.....48882277
%C ..64..432.1009..4816..45988..294924..1500288..10862979....74522808....445537503
%C .128.1088.2697.15697.205950.1719748.10862979.105482136...961899269...7444841268
%C .256.2944.7091.51711.912997.9770201.74522808.961899269.11448808957.111429411031
%H R. H. Hardin, <a href="/A304848/b304848.txt">Table of n, a(n) for n = 1..263</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5) for n>6
%F k=3: [order 11] for n>12
%F k=4: [order 34] for n>38
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..0..1..0. .0..0..1..1. .0..0..0..0. .0..1..0..0
%e ..0..1..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..0. .1..0..0..0
%e ..0..0..0..0. .0..0..0..0. .0..0..1..1. .1..0..0..0. .0..0..0..0
%e ..1..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..0..0. .0..0..0..1
%e ..0..1..0..0. .0..0..1..1. .1..1..1..1. .1..0..1..0. .0..0..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A303794.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, May 19 2018
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