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%I #4 Feb 04 2018 13:16:37
%S 1,2,2,4,7,4,8,13,13,8,16,29,20,29,16,32,69,27,27,69,32,64,137,47,75,
%T 47,137,64,128,301,83,191,191,83,301,128,256,705,137,401,626,401,137,
%U 705,256,512,1461,235,952,1442,1442,952,235,1461,512,1024,3193,412,2258,4115
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 6 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.......1024
%C ...2....7..13...29....69....137.....301.....705.....1461......3193.......7373
%C ...4...13..20...27....47.....83.....137.....235......412.......709.......1228
%C ...8...29..27...75...191....401.....952....2258.....5275.....13250......32268
%C ..16...69..47..191...626...1442....4115...12839....34387....101533.....306593
%C ..32..137..83..401..1442...3773...12847...48408...157805....562522....2057541
%C ..64..301.137..952..4115..12847...59287..270914..1088697...5017429...22861814
%C .128..705.235.2258.12839..48408..270914.1666826..8168186..46505377..277299195
%C .256.1461.412.5275.34387.157805.1088697.8168186.51863841.370258161.2763281188
%H R. H. Hardin, <a href="/A299187/b299187.txt">Table of n, a(n) for n = 1..220</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=5 k=4
%e ..0..1..0..1. .0..0..0..0. .0..0..1..0. .0..1..0..0. .0..0..1..1
%e ..0..0..0..1. .1..0..0..1. .1..1..0..1. .0..1..1..1. .1..0..1..0
%e ..0..0..1..0. .0..1..0..0. .0..0..0..1. .1..0..1..0. .1..1..1..0
%e ..1..0..0..1. .1..0..0..0. .1..0..1..0. .1..0..1..0. .1..1..1..0
%e ..1..1..0..1. .1..0..1..0. .1..0..1..0. .1..0..1..0. .1..0..0..1
%Y Column 1 is A000079(n-1).
%Y Column 2 is A297883.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 04 2018
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