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A280064 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%I A280064 #7 Feb 12 2019 12:16:15
%S A280064 1,2,5,15,39,104,281,771,2122,5858,16174,44694,123510,341403,943694,
%T A280064 2608709,7211359,19935055,55108220,152341402,421132682,1164181573,
%U A280064 3218268552,8896600238,24593808939,67987267220,187944382019,519554527901
%N A280064 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
%H A280064 R. H. Hardin, <a href="/A280064/b280064.txt">Table of n, a(n) for n = 1..210</a>
%F A280064 Empirical: a(n) = 3*a(n-1) + a(n-2) - 6*a(n-3) + 5*a(n-4) - 2*a(n-5) - 2*a(n-6) - a(n-7) for n>9.
%F A280064 Empirical g.f.: x*(1 + x)*(1 - 2*x + 4*x^3 - 8*x^4 + 2*x^5 - x^6 - x^7) / ((1 - x + x^2)*(1 - 2*x - 4*x^2 + 4*x^3 + 3*x^4 + x^5)). - _Colin Barker_, Feb 12 2019
%e A280064 Some solutions for n=4:
%e A280064 ..0..0..0. .0..1..1. .0..1..1. .0..0..0. .0..0..0. .0..0..0. .0..0..0
%e A280064 ..0..0..0. .0..1..1. .0..1..1. .0..0..0. .0..0..0. .1..1..0. .0..0..0
%e A280064 ..0..1..1. .0..1..1. .0..0..1. .0..0..1. .1..1..0. .1..1..0. .1..1..1
%e A280064 ..1..1..1. .0..0..0. .0..0..1. .0..1..1. .1..1..0. .1..0..0. .1..1..1
%Y A280064 Column 3 of A280069.
%K A280064 nonn
%O A280064 1,2
%A A280064 _R. H. Hardin_, Dec 25 2016