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%I #4 Feb 04 2018 13:28:36
%S 1,2,2,3,4,3,5,3,3,5,8,13,3,13,8,13,34,9,9,34,13,21,73,19,80,19,73,21,
%T 34,203,59,220,220,59,203,34,55,594,129,518,1539,518,129,594,55,89,
%U 1443,355,2466,3704,3704,2466,355,1443,89,144,4013,891,8609,25097,11459,25097
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 6 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
%C ..2....4...3....13.....34......73......203.......594.......1443.........4013
%C ..3....3...3.....9.....19......59......129.......355........891.........2317
%C ..5...13...9....80....220.....518.....2466......8609......26954.......108253
%C ..8...34..19...220...1539....3704....25097....161188.....638942......3784977
%C .13...73..59...518...3704...11459....80188....533274....2432710.....15899938
%C .21..203.129..2466..25097...80188...848789...8080772...44495267....401953734
%C .34..594.355..8609.161188..533274..8080772.122310309..832353461..10703053961
%C .55.1443.891.26954.638942.2432710.44495267.832353461.6602925250.104043829095
%H R. H. Hardin, <a href="/A299194/b299194.txt">Table of n, a(n) for n = 1..199</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 17] for n>18
%F k=4: [order 69] for n>70
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..1..1..0. .0..1..1..0. .0..1..1..1. .0..0..1..0
%e ..0..0..0..0. .0..1..1..1. .1..0..1..1. .1..0..1..1. .1..1..1..1
%e ..1..1..1..1. .1..1..1..0. .0..0..1..0. .0..0..0..0. .1..1..1..1
%e ..0..0..1..1. .0..1..1..1. .0..0..1..1. .0..0..0..0. .0..0..1..0
%e ..1..1..1..0. .0..1..1..0. .1..1..1..0. .1..0..0..1. .0..0..0..1
%Y Column 1 is A000045(n+1).
%Y Column 2 is A297901.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 04 2018
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