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%I #4 Jul 22 2018 15:56:23
%S 1,2,2,3,5,3,5,9,9,5,8,21,14,21,8,13,57,29,29,57,13,21,125,73,105,73,
%T 125,21,34,289,165,379,379,165,289,34,55,741,394,1245,2345,1245,394,
%U 741,55,89,1737,1068,5458,9686,9686,5458,1068,1737,89,144,4045,3018,25315,65283
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..1....2....3......5.......8........13.........21...........34.............55
%C ..2....5....9.....21......57.......125........289..........741...........1737
%C ..3....9...14.....29......73.......165........394.........1068...........3018
%C ..5...21...29....105.....379......1245.......5458........25315.........111407
%C ..8...57...73....379....2345......9686......65283.......549872........3771839
%C .13..125..165...1245....9686.....69701.....887617.....10940249......123485236
%C .21..289..394...5458...65283....887617...20168266....403588059.....7455221517
%C .34..741.1068..25315..549872..10940249..403588059..13792577708...402260884943
%C .55.1737.3018.111407.3771839.123485236.7455221517.402260884943.18922956181705
%H R. H. Hardin, <a href="/A317160/b317160.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) -a(n-2) +8*a(n-3) -8*a(n-4)
%F k=3: [order 18] for n>20
%F k=4: [order 66] for n>69
%e Some solutions for n=5 k=4
%e ..0..1..1..1. .0..0..0..0. .0..1..1..1. .0..0..0..0. .0..0..0..0
%e ..0..0..1..1. .0..0..1..0. .1..1..1..1. .1..0..0..0. .1..0..0..0
%e ..0..0..1..0. .0..0..0..0. .1..1..1..1. .1..0..1..0. .1..1..0..0
%e ..1..0..1..0. .0..1..1..1. .1..1..1..1. .1..0..0..0. .1..1..0..1
%e ..0..0..1..1. .1..1..1..0. .0..1..1..1. .0..0..0..0. .0..1..0..0
%Y Column 1 is A000045(n+1).
%Y Column 2 is A304349.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jul 22 2018
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