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R. H. Hardin, <a href="/A305485/b305485.txt">Table of n, a(n) for n = 1..210</a>

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Number of nX4 0..1 arrays with every element unequal to 1, 2, 3, 6 or 8 king-move adjacent elements, with upper left element zero.

2, 33, 27, 65, 195, 125, 268, 1176, 805, 1681, 7276, 5844, 10771, 45897, 42168, 71400, 291373, 302289, 481228, 1860822, 2143789, 3279467, 11940222, 15053714, 22494177, 76946183, 104796222, 154849698, 497855289, 724251391, 1067769212, 3233541274

1,1

Column 4 of A305489.

Empirical: a(n) = 3*a(n-1) +4*a(n-3) -26*a(n-4) +29*a(n-6) +55*a(n-7) -18*a(n-8) -111*a(n-9) -15*a(n-10) +60*a(n-11) +72*a(n-12) -14*a(n-13) -36*a(n-14) -13*a(n-15) +5*a(n-16) +6*a(n-17) for n>22

Some solutions for n=5

..0..0..1..0. .0..1..1..1. .0..1..1..0. .0..1..0..0. .0..1..1..1

..0..1..1..0. .1..1..0..1. .0..0..1..0. .1..1..0..1. .1..1..0..1

..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1. .1..1..1..1

..1..0..0..0. .1..0..0..1. .1..1..0..0. .1..0..1..1. .0..0..1..1

..1..1..0..1. .1..1..0..1. .0..1..0..1. .1..0..0..1. .1..0..1..0

Cf. A305489.

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R. H. Hardin, Jun 02 2018

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