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

%I #4 May 05 2018 15:26:53

%S 0,5,14,69,376,1891,9889,51283,265582,1378735,7148318,37076755,

%T 192302847,997352273,5172817910,26828692621,139146758064,721683805709,

%U 3743005199161,19413064725327,100685681893488,522205367420747

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

%C Column 3 of A304065.

%H R. H. Hardin, <a href="/A304060/b304060.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +14*a(n-2) +3*a(n-3) -75*a(n-4) -79*a(n-5) +61*a(n-6) +113*a(n-7) +38*a(n-8) -21*a(n-9) +5*a(n-10) +23*a(n-11) -6*a(n-12) -8*a(n-13) +4*a(n-14) for n>16

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A304065.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 05 2018