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A281766 Number of 2 X n 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%I A281766 #7 Feb 20 2019 10:19:36
%S A281766 0,4,14,40,110,280,698,1696,4052,9564,22330,51728,118998,272228,
%T A281766 619804,1405456,3175966,7155320,16078698,36048008,80656900,180149700,
%U A281766 401740002,894646944,1989842814,4420825196,9811946668,21757950712,48209235558
%N A281766 Number of 2 X n 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%H A281766 R. H. Hardin, <a href="/A281766/b281766.txt">Table of n, a(n) for n = 1..210</a>
%F A281766 Empirical: a(n) = 4*a(n-1) + a(n-2) - 16*a(n-3) - a(n-4) + 30*a(n-5) + 4*a(n-6) - 24*a(n-7) - 4*a(n-8) + 8*a(n-9).
%F A281766 Empirical g.f.: 2*x^2*(1 - x)*(1 + x)*(2 - x - 8*x^2 - x^3 + 6*x^4) / ((1 - 2*x)*(1 - x - 3*x^2 + 2*x^4)^2). - _Colin Barker_, Feb 20 2019
%e A281766 Some solutions for n=4:
%e A281766 ..0..1..1..1. .0..0..0..0. .0..0..1..0. .0..1..0..0. .0..0..0..1
%e A281766 ..0..0..0..0. .0..1..1..1. .0..1..0..1. .1..1..1..0. .0..0..0..0
%Y A281766 Row 2 of A281765.
%K A281766 nonn
%O A281766 1,2
%A A281766 _R. H. Hardin_, Jan 29 2017