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Number of nX3 0..1 arrays with every element unequal to 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.
1

%I #4 May 31 2018 09:16:11

%S 1,16,39,107,310,943,2935,9077,28054,87562,272571,850365,2654831,

%T 8284969,25870031,80782480,252246425,787748512,2460025106,7682422987,

%U 23991929280,74925446720,233989461442,730741987475,2282083022643,7126881707392

%N Number of nX3 0..1 arrays with every element unequal to 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A305367.

%H R. H. Hardin, <a href="/A305362/b305362.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +5*a(n-2) +2*a(n-3) -16*a(n-4) -14*a(n-5) -27*a(n-7) +32*a(n-8) +52*a(n-9) +43*a(n-10) +27*a(n-11) -34*a(n-12) -25*a(n-13) -12*a(n-14) +13*a(n-15) +a(n-16) -20*a(n-17) -8*a(n-18)

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A305367.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 31 2018