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%I #4 Jan 19 2018 08:05:05
%S 1,1,1,1,1,1,1,1,1,1,1,2,11,2,1,1,5,2,2,5,1,1,9,27,7,27,9,1,1,22,36,
%T 34,34,36,22,1,1,45,86,105,214,105,86,45,1,1,101,162,406,1270,1270,
%U 406,162,101,1,1,218,368,1504,3963,10681,3963,1504,368,218,1,1,477,727,6183
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5 or 6 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..11....2.....27......36........86........162..........368...........727
%C .1...2...2....7.....34.....105.......406.......1504.........6183.........25013
%C .1...5..27...34....214....1270......3963......22290.......109407........575051
%C .1...9..36..105...1270...10681.....72509.....692536......6184710......57152783
%C .1..22..86..406...3963...72509....610525....9392919....119508030....1732328018
%C .1..45.162.1504..22290..692536...9392919..240137045...5101146140..120394407026
%C .1.101.368.6183.109407.6184710.119508030.5101146140.176490627544.6773268608554
%H R. H. Hardin, <a href="/A298444/b298444.txt">Table of n, a(n) for n = 1..197</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: [order 12] for n>13
%F k=4: [order 34] for n>36
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..0..1..1. .0..1..1..1. .0..0..1..1. .0..0..1..1
%e ..1..1..1..1. .0..0..1..1. .1..1..1..1. .0..0..1..1. .0..0..1..1
%e ..1..0..1..0. .0..0..1..0. .1..1..0..0. .1..0..1..1. .0..1..1..1
%e ..1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1
%e ..0..1..1..1. .1..1..1..1. .0..0..0..1. .0..0..0..0. .0..0..1..1
%Y Column 2 is A052962(n-2).
%K nonn,tabl
%O 1,12
%A _R. H. Hardin_, Jan 19 2018
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