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%I #4 May 30 2018 17:07:40
%S 1,2,2,3,5,3,5,9,9,5,8,21,14,21,8,13,53,28,28,53,13,21,105,63,77,63,
%T 105,21,34,237,126,199,199,126,237,34,55,577,245,454,649,454,245,577,
%U 55,89,1205,505,1074,1729,1729,1074,505,1205,89,144,2681,1037,2619,4685,5408
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..1....2....3....5.....8.....13.....21......34.......55........89.......144
%C ..2....5....9...21....53....105....237.....577.....1205......2681......6349
%C ..3....9...14...28....63....126....245.....505.....1037......2088......4230
%C ..5...21...28...77...199....454...1074....2619.....6216.....14782.....35494
%C ..8...53...63..199...649...1729...4685...13671....38115....105379....298557
%C .13..105..126..454..1729...5408..17054...58109...187782....603230...1995190
%C .21..237..245.1074..4685..17054..64658..259281...981360...3731097..14545752
%C .34..577..505.2619.13671..58109.259281.1241359..5567478..25026350.115911873
%C .55.1205.1037.6216.38115.187782.981360.5567478.29268593.154351497.843143816
%H R. H. Hardin, <a href="/A305347/b305347.txt">Table of n, a(n) for n = 1..391</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = a(n-1) +8*a(n-3) -4*a(n-4)
%F k=3: [order 12]
%F k=4: [order 36] for n>37
%F k=5: [order 37] for n>48
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..1..1. .0..1..1..0. .0..1..1..1. .0..0..1..1
%e ..0..1..0..0. .0..1..1..1. .1..1..1..1. .1..1..1..1. .0..1..1..1
%e ..1..1..1..0. .1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
%e ..1..1..0..0. .1..1..1..1. .1..1..1..0. .1..1..1..1. .1..1..1..1
%e ..1..0..0..0. .1..0..1..1. .1..1..0..0. .1..0..1..1. .1..1..0..1
%Y Column 1 is A000045(n+1).
%Y Column 2 is A303963.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, May 30 2018
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