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%I #4 Jan 08 2018 07:07:03
%S 1,2,2,3,4,3,5,3,3,5,8,13,1,13,8,13,34,4,4,34,13,21,73,5,37,5,73,21,
%T 34,203,5,54,54,5,203,34,55,594,20,97,281,97,20,594,55,89,1443,29,466,
%U 395,395,466,29,1443,89,144,4013,63,1105,2353,257,2353,1105,63,4013,144,233
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 4 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....4..3...13....34....73....203.....594.....1443......4013......11114
%C ..3....3..1....4.....5.....5.....20......29.......63.......156........311
%C ..5...13..4...37....54....97....466....1105.....3354.....12282......37107
%C ..8...34..5...54...281...395...2353...12834....42557....215887....1120924
%C .13...73..5...97...395...257...1586....5761....18420.....89795.....363173
%C .21..203.20..466..2353..1586..23911..117161...369290...3815083...22352269
%C .34..594.29.1105.12834..5761.117161.1367645..4265928..59508287..657006826
%C .55.1443.63.3354.42557.18420.369290.4265928.10485521.149524668.1517719548
%H R. H. Hardin, <a href="/A297907/b297907.txt">Table of n, a(n) for n = 1..220</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) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6
%F k=3: [order 12] for n>13
%F k=4: [order 48] for n>51
%e Some solutions for n=7 k=4
%e ..0..1..0..1. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..0..1
%e ..1..0..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .1..1..0..0
%e ..1..1..0..1. .0..1..1..1. .1..1..0..1. .1..1..0..1. .1..1..0..1
%e ..0..1..0..1. .1..0..1..0. .1..0..0..1. .0..1..0..1. .0..1..0..0
%e ..0..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..1..0..0
%e ..1..1..0..1. .1..0..1..1. .1..1..1..0. .1..1..0..1. .1..1..1..1
%e ..0..1..1..0. .1..0..1..1. .0..1..0..1. .1..1..0..1. .0..1..0..0
%Y Column 1 is A000045(n+1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 08 2018
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