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Number of nX3 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
1

%I #4 Aug 24 2018 11:01:39

%S 4,10,20,36,76,160,344,748,1624,3544,7724,16856,36776,80252,175128,

%T 382168,833996,1819992,3971720,8667356,18914520,41276600,90076716,

%U 196571800,428972904,936135100,2042900376,4458162072,9728917388

%N Number of nX3 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Column 3 of A318343.

%H R. H. Hardin, <a href="/A318338/b318338.txt">Table of n, a(n) for n = 1..210</a>

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

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A318343.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 24 2018