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A317465 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 7

%I

%S 0,0,0,0,3,0,0,5,5,0,0,18,16,18,0,0,61,107,107,61,0,0,209,636,1429,

%T 636,209,0,0,702,3893,16809,16809,3893,702,0,0,2381,23769,203786,

%U 386855,203786,23769,2381,0,0,8069,145280,2461839,9178195,9178195,2461839

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .0....0......0.........0............0..............0.................0

%C .0....3......5........18...........61............209...............702

%C .0....5.....16.......107..........636...........3893.............23769

%C .0...18....107......1429........16809.........203786...........2461839

%C .0...61....636.....16809.......386855........9178195.........217053933

%C .0..209...3893....203786......9178195......426934467.......19791556259

%C .0..702..23769...2461839....217053933....19791556259.....1798167135483

%C .0.2381.145280..29797355...5142922330...919311610591...163704740864606

%C .0.8069.887980.360606527.121842389647.42696124087673.14901625879985868

%H R. H. Hardin, <a href="/A317465/b317465.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6

%F k=3: [order 12] for n>14

%F k=4: [order 28] for n>29

%F k=5: [order 61] for n>64

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A303684.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jul 28 2018

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Last modified January 16 18:07 EST 2022. Contains 350376 sequences. (Running on oeis4.)