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A280174 Number of n X 2 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%I A280174 #9 Feb 13 2019 08:17:58
%S A280174 1,2,12,41,103,263,656,1618,3931,9459,22557,53395,125594,293796,
%T A280174 683972,1585588,3661900,8428646,19341455,44261305,101034472,230100558,
%U A280174 522936849,1186138105,2685582035,6070360107,13699764020,30873005212,69478759648
%N A280174 Number of n X 2 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
%H A280174 R. H. Hardin, <a href="/A280174/b280174.txt">Table of n, a(n) for n = 1..210</a>
%F A280174 Empirical: a(n) = 4*a(n-1) - 11*a(n-3) - 4*a(n-4) + 15*a(n-5) + 14*a(n-6) - 2*a(n-7) - 9*a(n-8) - 5*a(n-9) - a(n-10) for n>14.
%F A280174 Empirical g.f.: x*(1 - 2*x + 4*x^2 + 4*x^3 - 35*x^4 - 24*x^5 + 59*x^6 + 85*x^7 - 6*x^8 - 69*x^9 - 43*x^10 - 5*x^11 + 3*x^12 + x^13) / ((1 - x)*(1 - x - 2*x^2 - x^3)^3). - _Colin Barker_, Feb 13 2019
%e A280174 Some solutions for n=4:
%e A280174 ..0..0. .0..0. .0..0. .0..1. .0..0. .0..1. .0..1. .0..1. .0..1. .0..0
%e A280174 ..0..1. .0..0. .0..1. .1..1. .0..0. .0..1. .0..0. .0..0. .0..0. .0..1
%e A280174 ..0..1. .0..1. .0..0. .1..1. .1..1. .0..0. .1..0. .0..0. .0..0. .0..1
%e A280174 ..0..0. .0..1. .0..1. .0..1. .0..1. .0..0. .0..0. .1..1. .1..0. .1..1
%Y A280174 Column 2 of A280180.
%K A280174 nonn
%O A280174 1,2
%A A280174 _R. H. Hardin_, Dec 28 2016