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A281199 Number of n X 2 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%I A281199 #7 Feb 16 2019 11:14:28
%S A281199 0,2,10,38,130,420,1308,3970,11822,34690,100610,289032,823800,2332418,
%T A281199 6566290,18394910,51310978,142587180,394905492,1090444930,3002921270,
%U A281199 8249479162,22612505090,61857842448,168903452400,460409998850
%N A281199 Number of n X 2 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%H A281199 R. H. Hardin, <a href="/A281199/b281199.txt">Table of n, a(n) for n = 1..210</a>
%F A281199 Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).
%F A281199 Conjectures from _Colin Barker_, Feb 16 2019: (Start)
%F A281199 G.f.: 2*x^2*(1 - x) / (1 - 3*x + x^2)^2.
%F A281199 a(n) = (2^(-n)*(2*sqrt(5)*((3-sqrt(5))^n - (3+sqrt(5))^n) - 5*(3-sqrt(5))^n*(1+sqrt(5))*n + 5*(-1+sqrt(5))*(3+sqrt(5))^n*n)) / 25.
%F A281199 (End)
%e A281199 Some solutions for n=4:
%e A281199 ..0..1. .0..0. .0..0. .0..1. .0..1. .0..1. .0..1. .0..1. .0..0. .0..1
%e A281199 ..0..0. .1..0. .1..1. .0..0. .1..1. .0..1. .0..1. .1..0. .0..1. .1..1
%e A281199 ..0..1. .0..1. .0..1. .0..1. .0..0. .1..0. .1..1. .0..1. .0..0. .0..1
%e A281199 ..1..0. .1..1. .1..1. .0..1. .1..0. .0..0. .0..0. .1..1. .1..0. .0..0
%Y A281199 Column 2 of A281205.
%K A281199 nonn
%O A281199 1,2
%A A281199 _R. H. Hardin_, Jan 17 2017