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%I #10 May 09 2022 00:18:47
%S 2,6,11,28,63,139,328,735,1684,3853,8750,20021,45627,104068,237541,
%T 541649,1235897,2819380,6431345,14672588,33470945,76356833,174191649,
%U 397374570,906523725,2068021039,4717711395,10762383681,24551876711
%N Number of n X 2 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 or 3 neighboring 1's.
%H R. H. Hardin, <a href="/A296390/b296390.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3) - a(n-4) + 4*a(n-5) - a(n-6) - 4*a(n-7) + a(n-9).
%F Empirical g.f.: x*(2 + 4*x + x^2 + x^3 + 3*x^4 - 4*x^5 - 4*x^6 + x^7 + x^8) / (1 - x - 2*x^2 - 2*x^3 + x^4 - 4*x^5 + x^6 + 4*x^7 - x^9). - _Colin Barker_, Feb 23 2019
%e Some solutions for n=5:
%e ..0..1. .1..1. .1..0. .0..0. .1..0. .0..0. .0..0. .0..1. .0..0. .0..0
%e ..0..1. .0..0. .1..0. .0..1. .1..1. .1..1. .1..0. .1..0. .1..1. .0..0
%e ..1..1. .1..1. .0..0. .0..1. .1..1. .0..0. .1..1. .0..0. .0..0. .0..0
%e ..1..0. .0..0. .1..1. .0..0. .0..1. .0..0. .1..1. .1..1. .0..1. .1..0
%e ..1..0. .1..1. .0..0. .1..1. .0..0. .1..1. .0..1. .0..0. .1..0. .1..0
%Y Column 2 of A296396.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 11 2017
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