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Number of nX3 0..1 arrays with every element unequal to 0, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
2

%I #4 May 12 2018 09:26:36

%S 1,8,23,103,520,2671,13876,72399,378321,1979531,10361881,54254622,

%T 284118654,1487964150,7792975441,40815315514,213770499606,

%U 1119631248273,5864130051553,30713754006040,160865382297683,842543809330756

%N Number of nX3 0..1 arrays with every element unequal to 0, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

%C Column 3 of A304419.

%H R. H. Hardin, <a href="/A304414/b304414.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +7*a(n-2) -16*a(n-3) -78*a(n-4) -11*a(n-5) +133*a(n-6) +161*a(n-7) +58*a(n-8) -114*a(n-9) -121*a(n-10) -91*a(n-11) -47*a(n-12) -12*a(n-13) +4*a(n-14) +8*a(n-15) for n>17

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A304419.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 12 2018