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%I #4 Dec 06 2017 08:38:17
%S 1,1,1,1,2,1,1,4,4,1,1,7,9,7,1,1,12,16,16,12,1,1,21,34,32,34,21,1,1,
%T 37,76,91,91,76,37,1,1,65,157,237,341,237,157,65,1,1,114,325,585,1150,
%U 1150,585,325,114,1,1,200,692,1513,3775,5171,3775,1513,692,200,1,1,351,1459
%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 3 or 5 king-move neighboring 1s.
%C Table starts
%C .1...1...1....1.....1......1.......1........1.........1..........1...........1
%C .1...2...4....7....12.....21......37.......65.......114........200.........351
%C .1...4...9...16....34.....76.....157......325.......692.......1459........3064
%C .1...7..16...32....91....237.....585.....1513......3908......10086.......26367
%C .1..12..34...91...341...1150....3775....12798.....43185.....146144......496975
%C .1..21..76..237..1150...5171...21087....90404....396578....1708355.....7449218
%C .1..37.157..585..3775..21087..108933...605121...3383481...18933967...108596954
%C .1..65.325.1513.12798..90404..605121..4342381..31360402..230562749..1738478648
%C .1.114.692.3908.43185.396578.3383481.31360402.296784399.2857761925.28501758381
%H R. H. Hardin, <a href="/A296157/b296157.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F k=3: [order 15]
%F k=4: [order 43]
%e Some solutions for n=7 k=4
%e ..0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1
%e ..1..1..1..1. .1..1..1..1. .0..1..1..0. .1..1..1..1. .1..1..1..1
%e ..1..1..1..1. .1..1..1..1. .0..1..1..0. .0..0..0..0. .0..0..0..0
%e ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1
%e ..1..1..0..0. .0..1..1..0. .0..0..0..0. .1..1..1..1. .0..0..1..1
%e ..1..1..0..0. .0..1..1..0. .0..0..1..1. .1..1..1..1. .0..0..1..1
%e ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
%Y Column 2 is A005251(n+2).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Dec 06 2017
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