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%I #8 Feb 17 2019 16:54:16
%S 10,94,310,804,1906,4248,9118,19026,38916,78356,155834,306840,599204,
%T 1162074,2240438,4297644,8207494,15613762,29601530,55948952,105457480,
%U 198283598,371980528,696408816,1301351164,2427600480,4521378510
%N Number of n X 6 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 R. H. Hardin, <a href="/A281203/b281203.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 6*a(n-4) + 4*a(n-6) + 6*a(n-7) + 3*a(n-8) - 2*a(n-9) - 3*a(n-10) - 2*a(n-11) - a(n-12).
%F Empirical g.f.: 2*x*(1 + x)*(5 + 32*x + 14*x^2 - 43*x^3 - 55*x^4 - 31*x^5 + x^6 + 28*x^7 + 24*x^8 + 10*x^9 + 3*x^10) / (1 - x - 2*x^2 + x^4 + x^5 + x^6)^2. - _Colin Barker_, Feb 17 2019
%e Some solutions for n=4:
%e ..0..1..0..0..1..0. .0..0..1..0..1..0. .0..1..0..1..0..0. .0..0..1..0..1..0
%e ..0..1..1..0..1..0. .1..0..1..0..1..1. .1..0..1..0..1..0. .1..0..1..0..1..0
%e ..1..0..1..0..1..0. .0..1..0..1..0..1. .1..0..1..0..1..0. .1..0..1..0..1..0
%e ..0..1..0..1..0..1. .0..1..0..1..0..1. .1..0..1..0..1..0. .1..0..1..0..0..0
%Y Column 6 of A281205.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 17 2017
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