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

%I #7 Feb 15 2019 10:04:51

%S 0,0,6,24,92,318,1056,3406,10770,33542,103226,314634,951396,2857604,

%T 8534022,25360354,75037878,221184144,649773710,1903099818,5558851080,

%U 16197428578,47091498180,136634149236,395704051072,1144040493756

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

%H R. H. Hardin, <a href="/A281074/b281074.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 8*a(n-3) - 5*a(n-4) - 8*a(n-5) + 11*a(n-6) + a(n-8) + 6*a(n-9) - 2*a(n-10) - 4*a(n-11) - a(n-12).

%F Empirical g.f.: 2*x^3*(3 - 6*x + 7*x^2 - 9*x^3 - x^4 - 4*x^6 + x^7 + x^8) / ((1 - x)^2*(1 - 2*x - x^2 - 2*x^3 - 3*x^4 - x^5)^2). - _Colin Barker_, Feb 15 2019

%e Some solutions for n=4:

%e ..0..1. .0..0. .0..0. .0..0. .0..0. .0..1. .0..0. .0..1. .0..1. .0..0

%e ..1..0. .0..1. .1..1. .0..1. .0..1. .1..1. .1..1. .0..0. .0..1. .1..0

%e ..0..0. .0..0. .0..1. .0..0. .0..1. .0..1. .1..0. .1..0. .0..1. .1..0

%e ..1..0. .1..0. .1..1. .1..1. .1..0. .0..1. .1..0. .0..0. .1..1. .0..0

%Y Column 2 of A281080.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jan 14 2017