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%I #4 May 31 2018 09:19:49
%S 0,1,1,1,7,1,2,16,16,2,3,45,39,45,3,5,120,107,107,120,5,8,333,310,398,
%T 310,333,8,13,928,943,1532,1532,943,928,13,21,2613,2935,5465,7196,
%U 5465,2935,2613,21,34,7400,9077,21691,32765,32765,21691,9077,7400,34,55,21053
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0....1.....1......2.......3........5.........8.........13..........21
%C ..1....7....16.....45.....120......333.......928.......2613........7400
%C ..1...16....39....107.....310......943......2935.......9077.......28054
%C ..2...45...107....398....1532.....5465.....21691......82625......320130
%C ..3..120...310...1532....7196....32765....163682.....791180.....3881007
%C ..5..333...943...5465...32765...179644...1113793....6595796....39677540
%C ..8..928..2935..21691..163682..1113793...8803975...65762626...500606134
%C .13.2613..9077..82625..791180..6595796..65762626..615439372..5858512208
%C .21.7400.28054.320130.3881007.39677540.500606134.5858512208.69977566829
%H R. H. Hardin, <a href="/A305367/b305367.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) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6
%F k=3: [order 18]
%F k=4: [order 66] for n>68
%e Some solutions for n=5 k=4
%e ..0..1..0..0. .0..0..0..0. .0..1..0..0. .0..0..0..1. .0..1..1..1
%e ..1..0..1..0. .1..1..1..1. .1..0..1..0. .0..1..0..1. .1..1..1..0
%e ..1..0..1..1. .1..0..0..1. .1..1..0..1. .1..1..1..0. .1..1..1..1
%e ..1..0..0..1. .1..0..0..1. .0..1..1..0. .1..1..0..1. .0..0..1..0
%e ..1..1..0..1. .1..0..0..1. .1..1..1..0. .0..0..1..0. .1..0..0..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304013.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 31 2018
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