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Number of nX3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 2 or 4 neighboring 1s.
1

%I #4 Jan 03 2018 12:23:27

%S 5,26,95,415,1801,7526,32173,137242,583129,2484786,10583683,45062520,

%T 191933126,817441956,3481360348,14827246426,63149259874,268952155501,

%U 1145471423600,4878575547192,20777907778014,88493407078762

%N Number of nX3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 2 or 4 neighboring 1s.

%C Column 3 of A297694.

%H R. H. Hardin, <a href="/A297689/b297689.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) -2*a(n-2) +6*a(n-3) -52*a(n-4) +23*a(n-5) -3*a(n-6) +21*a(n-7) -9*a(n-8)

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A297694.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 03 2018