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%I #4 Jul 25 2018 11:19:05
%S 1,1,1,1,4,1,1,8,8,1,1,24,13,24,1,1,82,64,64,82,1,1,272,240,498,240,
%T 272,1,1,908,842,2922,2922,842,908,1,1,3076,3302,16877,31878,16877,
%U 3302,3076,1,1,10444,12740,111073,269286,269286,111073,12740,10444,1,1,35480,48468
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1.....1.....1.......1.........1...........1............1..............1
%C .1.....4.....8......24........82.........272..........908...........3076
%C .1.....8....13......64.......240.........842.........3302..........12740
%C .1....24....64.....498......2922.......16877.......111073.........700859
%C .1....82...240....2922.....31878......269286......2915690.......29663556
%C .1...272...842...16877....269286.....3234635.....52389467......773668467
%C .1...908..3302..111073...2915690....52389467...1396521994....32539573668
%C .1..3076.12740..700859..29663556...773668467..32539573668..1165304769027
%C .1.10444.48468.4405884.295164308.11290705493.748729425556.40989107393702
%H R. H. Hardin, <a href="/A317271/b317271.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) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
%F k=3: [order 20]
%F k=4: [order 71] for n>72
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..1..0..1. .0..1..1..1. .0..0..1..0. .0..0..1..0
%e ..1..0..1..0. .0..1..1..0. .0..1..0..0. .1..1..1..0. .1..1..1..0
%e ..1..1..1..0. .1..1..0..0. .1..1..1..1. .1..1..1..1. .0..1..1..0
%e ..1..0..1..1. .0..1..1..1. .1..0..1..0. .0..0..0..0. .0..1..1..0
%e ..0..1..1..0. .0..1..1..1. .1..0..1..0. .1..1..1..1. .1..0..0..1
%Y Column 2 is A303882.
%Y Column 3 is A306131.
%Y Column 4 is A306132.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jul 25 2018
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