%I #7 Jun 08 2018 03:06:04
%S 0,1,1,1,3,1,2,2,2,2,3,1,3,1,3,5,8,5,5,8,5,8,5,6,4,6,5,8,13,22,14,13,
%T 13,14,22,13,21,29,22,30,62,30,22,29,21,34,60,33,43,88,88,43,33,60,34,
%U 55,121,57,129,339,237,339,129,57,121,55,89,194,97,245,888,685,685,888,245
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0..1..1...2....3....5.....8.....13.....21......34.......55.......89.......144
%C ..1..3..2...1....8....5....22.....29.....60.....121......194......425.......704
%C ..1..2..3...5....6...14....22.....33.....57......97......159......255.......432
%C ..2..1..5...4...13...30....43....129....245.....519.....1254.....2525......5707
%C ..3..8..6..13...62...88...339....888...2108....6329....16064....43396....117393
%C ..5..5.14..30...88..237...685...1827...4974...14425....38170...106811....300976
%C ..8.22.22..43..339..685..2673..11690..31390..133744...470762..1540068...6102146
%C .13.29.33.129..888.1827.11690..47501.161251..821454..3119449.12780462..56341952
%C .21.60.57.245.2108.4974.31390.161251.555463.3235101.14367171.61271388.319305797
%H R. H. Hardin, <a href="/A304302/b304302.txt">Table of n, a(n) for n = 1..480</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) for n>6
%F k=3: a(n) = a(n-2) +3*a(n-3) +2*a(n-4) -4*a(n-6) -2*a(n-7) -a(n-8) -2*a(n-9)
%F k=4: [order 15] for n>19
%F k=5: [order 32] for n>34
%F k=6: [order 64] for n>66
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..0..0..0. .0..1..0..0. .0..0..1..0. .0..0..0..0
%e ..1..0..0..0. .1..0..0..1. .0..0..0..1. .1..0..0..0. .1..0..0..1
%e ..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..0..0
%e ..1..0..0..1. .0..0..0..1. .0..0..0..1. .0..0..0..1. .1..0..0..0
%e ..0..0..0..0. .0..1..0..0. .0..1..0..0. .0..1..0..0. .0..0..1..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297809 for n>2.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 10 2018