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Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
1

%I #4 Jul 18 2018 19:31:34

%S 4,23,96,400,1704,7313,31328,134118,574442,2460748,10541124,45155605,

%T 193438738,828663631,3549885894,15207276051,65146190696,279078852182,

%U 1195542461428,5121570860689,21940242659146,93989578468682

%N Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A317011.

%H R. H. Hardin, <a href="/A317006/b317006.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) -7*a(n-3) -27*a(n-4) -5*a(n-5) +14*a(n-6) +78*a(n-7) +49*a(n-8) -46*a(n-9) -81*a(n-10) +5*a(n-11) +55*a(n-12) -2*a(n-13) -39*a(n-14) -30*a(n-15) -8*a(n-16) for n>17

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A317011.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 18 2018