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%I #9 Feb 15 2019 04:29:44
%S 0,0,2,12,58,252,1048,4204,16454,63236,239622,897792,3332864,12277952,
%T 44938282,163566412,592492026,2137194788,7680594760,27511516436,
%U 98254943022,349979793492,1243627373550,4409519905928,15603737422416
%N Number of n X 2 0..1 arrays with no element equal to more than three of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%H R. H. Hardin, <a href="/A281028/b281028.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 7*a(n-2) - 2*a(n-3) - 17*a(n-4) + 24*a(n-6) + 16*a(n-7) + 12*a(n-8) - 16*a(n-9) - 16*a(n-10).
%F Empirical g.f.: 2*x^3*(1 - 2*x^3)^2 / (1 - 3*x - x^2 - 2*x^3 + 2*x^4 + 4*x^5)^2. - _Colin Barker_, Feb 15 2019
%e Some solutions for n=4:
%e ..0..0. .0..0. .0..0. .0..0. .0..1. .0..0. .0..0. .0..1. .0..0. .0..1
%e ..0..1. .1..1. .1..0. .1..1. .1..1. .1..0. .0..1. .0..0. .1..0. .1..1
%e ..0..0. .0..1. .0..0. .1..0. .0..1. .0..0. .0..0. .0..1. .0..0. .1..0
%e ..0..1. .1..1. .1..1. .1..1. .1..1. .1..0. .1..0. .0..0. .0..1. .1..1
%Y Column 2 of A281034.
%K nonn
%O 1,3
%A _R. H. Hardin_, Jan 13 2017
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