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%I #4 Jan 20 2018 08:12:59
%S 1,2,2,3,4,3,5,3,3,5,8,13,1,13,8,13,34,4,4,34,13,21,73,5,38,5,73,21,
%T 34,203,6,54,54,6,203,34,55,594,20,97,281,97,20,594,55,89,1443,35,467,
%U 403,403,467,35,1443,89,144,4013,70,1105,2353,277,2353,1105,70,4013,144,233
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 7 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.....6.....20......35.......70.......174........365
%C ..5...13..4...38....54....97....467....1105.....3354.....12283......37107
%C ..8...34..5...54...281...403...2353...12942....43319....219059....1139692
%C .13...73..6...97...403...277...1602....6037....19001.....93205.....385257
%C .21..203.20..467..2353..1602..24272..118439...372820...3857775...22638601
%C .34..594.35.1105.12942..6037.118439.1377101..4336887..60191437..664833900
%C .55.1443.70.3354.43319.19001.372820.4336887.10659243.151971896.1550220630
%H R. H. Hardin, <a href="/A298501/b298501.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 15] for n>16
%F k=4: [order 51] for n>54
%e Some solutions for n=6 k=4
%e ..0..1..0..1. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..0..0..1
%e ..1..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..1..1. .1..1..0..0
%e ..1..1..0..1. .1..1..1..1. .0..1..0..0. .1..0..1..0. .1..1..1..0
%e ..1..1..0..1. .0..0..0..0. .0..1..0..1. .1..0..1..1. .0..0..0..1
%e ..0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..1..0. .0..0..1..1
%e ..1..1..0..1. .1..1..1..1. .1..1..0..0. .1..0..0..1. .1..1..1..0
%Y Column 1 is A000045(n+1).
%Y Column 2 is A297901.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 20 2018
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