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%I #6 Apr 21 2021 15:07:14
%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 43,137,64,128,301,72,130,130,72,301,128,256,705,115,233,310,233,115,
%U 705,256,512,1461,189,448,531,531,448,189,1461,512,1024,3193,318,877,1112
%N T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 4, 6 or 8 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..310..531..1112..2418...4870..10382...21883...45941...97484
%C ..32..137..72..233..531.1002..1852..4200...9436..19203...41599...91092..197402
%C ..64..301.115..448.1112.1852..4929.11412..24191..59037..137098..312216..728670
%C .128..705.189..877.2418.4200.11412.28917..66656.169277..416130..999147.2499437
%C .256.1461.318.1605.4870.9436.24191.66656.170693.444484.1173512.3002664.7845019
%H R. H. Hardin, <a href="/A299388/b299388.txt">Table of n, a(n) for n = 1..310</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=7
%e ..0..0..0..1..1..0..0. .0..0..0..1..1..0..0. .0..1..1..1..1..0..1
%e ..1..1..1..1..1..1..1. .1..1..1..0..0..1..1. .1..1..1..0..1..0..1
%e ..0..1..1..1..0..1..0. .0..0..0..0..1..0..1. .0..0..0..0..1..1..0
%e ..0..1..1..1..0..0..1. .1..0..0..0..0..1..1. .1..0..0..0..1..1..1
%e ..1..1..1..1..1..1..0. .1..0..0..0..1..1..1. .1..0..0..0..0..1..1
%e ..1..1..0..0..0..1..1. .0..0..0..0..1..1..0. .1..0..1..1..1..1..0
%e ..1..0..1..1..1..0..0. .1..1..1..0..1..0..1. .0..1..0..0..0..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A297883.
%Y Column 3 is A298289.
%Y Column 4 is A298290.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 09 2018
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