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%I #4 Feb 13 2018 11:25:52
%S 1,1,1,1,1,1,1,1,1,1,1,2,10,2,1,1,5,10,10,5,1,1,9,27,19,27,9,1,1,22,
%T 63,43,43,63,22,1,1,45,115,126,172,126,115,45,1,1,101,267,327,616,616,
%U 327,267,101,1,1,218,569,860,1734,2597,1734,860,569,218,1,1,477,1193,2401
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1...1...1....1.....1......1.......1........1..........1...........1
%C .1...1...1....2.....5......9......22.......45........101.........218
%C .1...1..10...10....27.....63.....115......267........569........1193
%C .1...2..10...19....43....126.....327......860.......2401........6733
%C .1...5..27...43...172....616....1734.....6188......22944.......81842
%C .1...9..63..126...616...2597...10646....56122.....291690.....1619418
%C .1..22.115..327..1734..10646...61273...464681....3999592....35862058
%C .1..45.267..860..6188..56122..464681..6245870...83493860..1154724040
%C .1.101.569.2401.22944.291690.3999592.83493860.1821672943.40042035336
%H R. H. Hardin, <a href="/A299581/b299581.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +3*a(n-2) -2*a(n-4) for n>5
%F k=3: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -4*a(n-4) -2*a(n-5) -2*a(n-6) +a(n-9) for n>13
%F k=4: [order 34]
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..1..1. .0..1..1..0. .0..0..0..0. .0..1..1..1
%e ..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .1..1..1..1
%e ..0..0..0..0. .1..0..1..0. .1..1..1..1. .0..0..0..0. .1..1..1..0
%e ..1..1..1..1. .0..0..1..1. .1..1..1..1. .0..0..0..0. .1..1..1..1
%e ..1..1..1..1. .0..0..1..1. .1..1..1..1. .0..0..0..0. .0..1..1..1
%Y Column 2 is A052962(n-2).
%K nonn,tabl
%O 1,12
%A _R. H. Hardin_, Feb 13 2018
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