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A316641 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero. 7

%I

%S 0,1,1,1,7,1,2,16,16,2,3,45,43,45,3,5,120,122,122,120,5,8,333,404,524,

%T 404,333,8,13,928,1344,2342,2342,1344,928,13,21,2613,4583,9773,14568,

%U 9773,4583,2613,21,34,7400,15737,44095,85222,85222,44095,15737,7400,34

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5, 7 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....43....122......404......1344.......4583........15737.........53378

%C ..2...45...122....524.....2342......9773......44095.......195387........864584

%C ..3..120...404...2342....14568.....85222.....532401......3294736......20347911

%C ..5..333..1344...9773....85222....684269....5879970.....50360206.....428319949

%C ..8..928..4583..44095...532401...5879970...69857903....835457349....9913271027

%C .13.2613.15737.195387..3294736..50360206..835457349..14106315869..235116618481

%C .21.7400.53378.864584.20347911.428319949.9913271027.235116618481.5489873419154

%H R. H. Hardin, <a href="/A316641/b316641.txt">Table of n, a(n) for n = 1..180</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 19] for n>21

%F k=4: [order 69] for n>71

%e Some solutions for n=5 k=4

%e ..0..0..0..1. .0..1..1..1. .0..1..0..1. .0..0..0..0. .0..0..0..0

%e ..1..0..1..1. .0..1..1..0. .1..1..1..1. .1..0..0..1. .1..1..1..0

%e ..0..0..0..1. .1..0..1..1. .0..1..1..0. .0..0..0..0. .1..1..1..0

%e ..1..0..0..0. .1..1..1..1. .0..0..1..1. .0..0..0..1. .1..0..0..0

%e ..0..0..0..1. .0..1..1..0. .0..1..1..0. .1..0..1..1. .0..0..1..0

%Y Column 1 is A000045(n-1).

%Y Column 2 is A304013.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jul 09 2018

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Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)