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%I #4 Feb 19 2018 15:44:08
%S 1,1,1,1,5,1,1,13,13,1,1,42,39,42,1,1,127,202,202,127,1,1,389,894,
%T 2101,894,389,1,1,1192,4507,18101,18101,4507,1192,1,1,3645,22684,
%U 176353,302780,176353,22684,3645,1,1,11161,116651,1735393,5678641,5678641
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1.....1......1.........1...........1.............1................1
%C .1.....5.....13........42.........127...........389.............1192
%C .1....13.....39.......202.........894..........4507............22684
%C .1....42....202......2101.......18101........176353..........1735393
%C .1...127....894.....18101......302780.......5678641........107544794
%C .1...389...4507....176353.....5678641.....203062719.......7338573888
%C .1..1192..22684...1735393...107544794....7338573888.....506116118801
%C .1..3645.116651..17279857..2047783162..266405977942...35028322225854
%C .1.11161.605727.173340585.39237426288.9728685869763.2438361076801151
%H R. H. Hardin, <a href="/A299821/b299821.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +5*a(n-2) +4*a(n-3)
%F k=3: [order 14] for n>16
%F k=4: [order 38] for n>39
%e Some solutions for n=5 k=4
%e ..0..1..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..1
%e ..1..1..1..1. .0..1..1..1. .0..0..1..0. .0..0..0..0. .0..0..1..1
%e ..0..1..1..1. .0..0..0..0. .0..1..1..1. .0..0..0..0. .1..0..0..0
%e ..1..1..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..0. .0..0..0..0
%e ..1..0..0..1. .0..0..0..0. .0..1..1..1. .1..0..1..1. .1..0..0..0
%Y Column 2 is A298234.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Feb 19 2018
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