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%I #4 Feb 26 2018 08:11:33
%S 0,1,1,0,4,0,1,4,4,1,0,16,1,16,0,1,48,18,18,48,1,0,88,41,246,41,88,0,
%T 1,240,130,1043,1043,130,240,1,0,704,510,5368,13182,5368,510,704,0,1,
%U 1600,1740,37739,78147,78147,37739,1740,1600,1,0,4032,5554,219689,913701
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5, 6, 7 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......18.......41........130..........510...........1740
%C .1...16...18.....246.....1043.......5368........37739.........219689
%C .0...48...41....1043....13182......78147.......913701.......11122233
%C .1...88..130....5368....78147....1048462.....21602016......399714825
%C .0..240..510...37739...913701...21602016....783899343....25183985328
%C .1..704.1740..219689.11122233..399714825..25183985328..1507189100633
%C .0.1600.5554.1245482.99027295.6588098950.731705422933.74614900420199
%H R. H. Hardin, <a href="/A300146/b300146.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 15] for n>17
%F k=4: [order 40] for n>42
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..1. .0..1..1..1
%e ..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..1. .1..0..1..1
%e ..0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0
%e ..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1. .0..1..0..0
%e ..0..0..0..0. .1..1..0..0. .0..0..1..1. .1..1..0..0. .1..0..0..0
%Y Column 2 is A298448.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Feb 26 2018
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