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%I #4 May 11 2018 14:25:18
%S 1,2,2,3,5,3,5,9,9,5,8,21,13,21,8,13,57,27,27,57,13,21,125,60,101,60,
%T 125,21,34,289,123,333,333,123,289,34,55,741,280,1023,1540,1023,280,
%U 741,55,89,1737,729,4370,5153,5153,4370,729,1737,89,144,4045,2015,19555,34887
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4 or 5 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...13....27......60......123........280..........729..........2015
%C ..5...21...27...101.....333.....1023.......4370........19555.........81921
%C ..8...57...60...333....1540.....5153......34887.......269948.......1656222
%C .13..125..123..1023....5153....36201.....445745......4761156......49676930
%C .21..289..280..4370...34887...445745....9176798....160397426....2593742186
%C .34..741..729.19555..269948..4761156..160397426...4663483164..115363289438
%C .55.1737.2015.81921.1656222.49676930.2593742186.115363289438.4502196415629
%H R. H. Hardin, <a href="/A304355/b304355.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..0..0..0. .0..1..1..0. .0..1..1..1. .0..0..1..1. .0..0..0..0
%e ..1..0..0..1. .1..1..1..1. .1..1..1..1. .0..0..0..1. .1..0..0..1
%e ..1..0..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
%e ..1..0..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
%e ..0..0..1..0. .1..1..0..1. .0..1..1..0. .0..1..0..0. .0..1..0..0
%Y Column 1 is A000045(n+1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, May 11 2018
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