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%I #4 Jun 28 2018 15:34:40
%S 1,2,2,4,8,4,8,21,21,8,16,49,42,49,16,32,120,125,125,120,32,64,293,
%T 361,354,361,293,64,128,719,987,1372,1372,987,719,128,256,1774,2840,
%U 3933,7973,3933,2840,1774,256,512,4389,8177,12454,35706,35706,12454,8177,4389
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2.....4......8......16.......32........64.........128..........256
%C ...2....8....21.....49.....120......293.......719........1774.........4389
%C ...4...21....42....125.....361......987......2840........8177........23078
%C ...8...49...125....354....1372.....3933.....12454.......42946.......135396
%C ..16..120...361...1372....7973....35706....164734......838632......4054621
%C ..32..293...987...3933...35706...205946...1262767.....8828402.....57330292
%C ..64..719..2840..12454..164734..1262767..10464990...101136854....901515338
%C .128.1774..8177..42946..838632..8828402.101136854..1363011634..17053088411
%C .256.4389.23078.135396.4054621.57330292.901515338.17053088411.297013482603
%H R. H. Hardin, <a href="/A316289/b316289.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) +a(n-2) -4*a(n-3) -4*a(n-4) for n>5
%F k=3: [order 10] for n>12
%F k=4: [order 21] for n>25
%F k=5: [order 85] for n>89
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..1..0. .0..1..1..0. .0..0..0..0. .0..0..0..0
%e ..0..0..0..1. .0..0..1..1. .1..1..1..1. .0..1..1..0. .0..1..0..0
%e ..0..0..1..1. .0..0..0..0. .1..1..1..1. .0..0..1..0. .0..0..0..0
%e ..0..1..1..1. .1..0..0..0. .1..0..1..1. .0..0..0..0. .0..0..1..0
%e ..1..1..1..0. .1..1..0..1. .1..1..1..1. .1..0..0..0. .0..1..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A303721.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jun 28 2018
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