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%I #4 Jan 12 2018 09:02:37
%S 0,0,0,0,1,0,0,3,3,0,0,2,0,2,0,0,11,3,3,11,0,0,13,1,10,1,13,0,0,34,7,
%T 28,28,7,34,0,0,65,18,76,154,76,18,65,0,0,123,52,213,520,520,213,52,
%U 123,0,0,266,144,645,1574,2767,1574,645,144,266,0,0,499,405,1852,7204,11202
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0...0...0....0.....0......0.......0........0.........0..........0...........0
%C .0...1...3....2....11.....13......34.......65.......123........266.........499
%C .0...3...0....3.....1......7......18.......52.......144........405........1124
%C .0...2...3...10....28.....76.....213......645......1852.......5642.......17016
%C .0..11...1...28...154....520....1574.....7204.....28790.....105055......437163
%C .0..13...7...76...520...2767...11202....66148....385999....2040394....11280309
%C .0..34..18..213..1574..11202...65218...479206...3481050...24695892...177272585
%C .0..65..52..645..7204..66148..479206..4883926..46039875..420410890..3947485108
%C .0.123.144.1852.28790.385999.3481050.46039875.603770100.7267200831.90210295443
%H R. H. Hardin, <a href="/A298087/b298087.txt">Table of n, a(n) for n = 1..219</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)
%F k=3: [order 16] for n>17
%F k=4: [order 57] for n>58
%e Some solutions for n=7 k=4
%e ..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0
%e ..0..1..0..1. .0..1..0..1. .1..0..1..1. .0..1..0..1. .0..1..1..0
%e ..1..1..0..1. .1..0..0..1. .1..1..1..1. .1..0..1..0. .1..0..1..0
%e ..0..0..1..1. .0..1..0..1. .0..0..1..1. .1..0..1..0. .1..0..1..0
%e ..0..0..0..0. .0..1..1..1. .0..1..0..0. .1..0..1..0. .1..0..1..0
%e ..0..0..1..0. .1..0..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1
%e ..0..0..1..1. .1..1..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..1
%Y Column 2 is A297870.
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_, Jan 12 2018
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