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Number of nX3 0..1 arrays with every element unequal to 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
1

%I #4 Jun 01 2018 11:01:25

%S 1,11,7,20,44,77,181,379,849,1799,4154,9242,20384,46987,105477,238364,

%T 544013,1234035,2805803,6392808,14558529,33157368,75581441,172296118,

%U 392727236,895513084,2042029380,4656342833,10619040244,24217647660

%N Number of nX3 0..1 arrays with every element unequal to 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A305452.

%H R. H. Hardin, <a href="/A305447/b305447.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +3*a(n-2) +7*a(n-3) -6*a(n-4) -18*a(n-5) -26*a(n-6) +8*a(n-7) +27*a(n-8) +47*a(n-9) +16*a(n-10) -5*a(n-11) -3*a(n-12) -7*a(n-13) -20*a(n-14) -24*a(n-15) -5*a(n-16) -6*a(n-17) for n>18

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A305452.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jun 01 2018