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A281710 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%I A281710 #7 Feb 20 2019 05:35:07
%S A281710 1,7,8,14,17,22,30,43,64,98,153,242,386,619,996,1606,2593,4190,6774,
%T A281710 10955,17720,28666,46377,75034,121402,196427,317820,514238,832049,
%U A281710 1346278,2178318,3524587,5702896,9227474,14930361,24157826,39088178
%N A281710 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
%H A281710 R. H. Hardin, <a href="/A281710/b281710.txt">Table of n, a(n) for n = 1..210</a>
%F A281710 Empirical: a(n) = 2*a(n-1) - a(n-3) for n>6.
%F A281710 Empirical g.f.: x*(1 + 5*x - 6*x^2 - x^3 - 4*x^4 - 4*x^5) / ((1 - x)*(1 - x - x^2)). - _Colin Barker_, Feb 20 2019
%e A281710 Some solutions for n=4:
%e A281710 ..0..0..0. .0..0..0. .0..0..1. .0..0..1. .0..1..1. .0..0..1. .0..1..0
%e A281710 ..1..1..1. .0..0..0. .0..1..0. .0..1..0. .1..0..1. .0..1..0. .1..0..1
%e A281710 ..1..1..1. .0..0..0. .1..0..1. .1..0..1. .0..1..0. .1..0..1. .0..1..0
%e A281710 ..1..1..1. .1..1..1. .0..1..1. .0..1..0. .0..0..1. .1..1..0. .1..0..1
%Y A281710 Column 3 of A281715.
%K A281710 nonn
%O A281710 1,2
%A A281710 _R. H. Hardin_, Jan 28 2017