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%I #4 May 22 2018 11:19:14
%S 1,1,1,1,4,1,1,7,7,1,1,13,13,13,1,1,26,21,21,26,1,1,49,29,26,29,49,1,
%T 1,99,58,70,70,58,99,1,1,194,120,139,189,139,120,194,1,1,387,250,287,
%U 468,468,287,250,387,1,1,773,515,625,1436,1916,1436,625,515,773,1,1,1538
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1...1...1....1.....1.....1......1.......1........1........1.........1
%C .1...4...7...13....26....49.....99.....194......387......773......1538
%C .1...7..13...21....29....58....120.....250......515.....1100......2302
%C .1..13..21...26....70...139....287.....625.....1484.....3197......7321
%C .1..26..29...70...189...468...1436....3753....11101....32272.....92418
%C .1..49..58..139...468..1916...5296...17450....62128...207139....693887
%C .1..99.120..287..1436..5296..18950...76117...313593..1223755...4910872
%C .1.194.250..625..3753.17450..76117..401301..2043622..9772099..49480464
%C .1.387.515.1484.11101.62128.313593.2043622.12197817.69375211.421959328
%H R. H. Hardin, <a href="/A304952/b304952.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) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
%F k=3: [order 18] for n>19
%F k=4: [order 70] for n>71
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..1..1..0. .0..0..0..1. .0..1..1..0. .0..0..1..0
%e ..1..0..0..1. .1..1..0..1. .0..0..0..1. .1..0..1..1. .1..1..0..1
%e ..0..1..1..0. .1..0..1..0. .1..1..1..1. .1..1..1..0. .1..1..1..0
%e ..1..0..0..1. .0..0..1..0. .1..0..0..0. .0..0..1..1. .1..1..0..1
%e ..0..1..1..0. .1..1..0..1. .1..0..0..0. .1..0..0..0. .0..0..1..0
%Y Column 2 is A304004.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 22 2018
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