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%I #4 Feb 11 2018 06:22:38
%S 0,1,1,0,4,0,1,4,4,1,0,16,1,16,0,1,48,12,12,48,1,0,88,35,166,35,88,0,
%T 1,240,60,537,537,60,240,1,0,704,269,2573,7116,2573,269,704,0,1,1600,
%U 873,16538,26670,26670,16538,873,1600,1,0,4032,1985,83533,258389,278292
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0....1....0......1........0.........1...........0.............1
%C .1....4....4.....16.......48........88.........240...........704
%C .0....4....1.....12.......35........60.........269...........873
%C .1...16...12....166......537......2573.......16538.........83533
%C .0...48...35....537.....7116.....26670......258389.......3071901
%C .1...88...60...2573....26670....278292.....4719927......71687832
%C .0..240..269..16538...258389...4719927...135080376....3421183432
%C .1..704..873..83533..3071901..71687832..3421183432..167282094170
%C .0.1600.1985.420801.19928263.922790506.75654324618.5847633932248
%H R. H. Hardin, <a href="/A299528/b299528.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-2)
%F k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)
%F k=3: [order 17] for n>18
%F k=4: [order 53] for n>56
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..1..0..0
%e ..0..1..0..1. .0..0..1..1. .1..1..0..0. .0..0..0..0. .0..1..0..0
%e ..1..1..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..0. .1..1..0..0
%e ..1..1..0..0. .1..1..1..1. .1..1..0..1. .0..1..1..0. .1..1..1..0
%e ..1..1..0..0. .0..0..1..1. .1..1..0..1. .0..1..1..0. .1..1..0..1
%Y Column 2 is A298448.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Feb 11 2018
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