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%I #4 May 22 2018 11:26:34
%S 0,1,1,1,7,1,2,16,16,2,3,45,42,45,3,5,120,118,118,120,5,8,333,371,496,
%T 371,333,8,13,928,1203,2080,2080,1203,928,13,21,2613,3917,8361,11282,
%U 8361,3917,2613,21,34,7400,12919,35441,60568,60568,35441,12919,7400,34
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0....1.....1......2........3.........5..........8..........13...........21
%C ..1....7....16.....45......120.......333........928........2613.........7400
%C ..1...16....42....118......371......1203.......3917.......12919........42060
%C ..2...45...118....496.....2080......8361......35441......148491.......621640
%C ..3..120...371...2080....11282.....60568.....334906.....1852576.....10208628
%C ..5..333..1203...8361....60568....435964....3174054....23304518....170481467
%C ..8..928..3917..35441...334906...3174054...30361694...294236689...2849022835
%C .13.2613.12919.148491..1852576..23304518..294236689..3805684538..49133027076
%C .21.7400.42060.621640.10208628.170481467.2849022835.49133027076.844100991906
%H R. H. Hardin, <a href="/A304959/b304959.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6
%F k=3: [order 20] for n>21
%F k=4: [order 69] for n>71
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..0..1..1. .0..0..1..1. .0..1..1..0. .0..0..0..1
%e ..0..0..0..1. .1..0..0..1. .0..1..0..0. .1..1..0..0. .1..0..0..0
%e ..1..1..0..1. .1..1..1..0. .0..1..1..0. .1..1..1..0. .0..0..0..1
%e ..0..1..1..0. .1..0..1..0. .1..0..0..1. .1..0..1..0. .0..0..1..1
%e ..0..0..0..0. .1..1..0..0. .1..0..1..1. .1..1..0..0. .1..0..1..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304013.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 22 2018
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