%I #8 Feb 23 2019 07:02:51
%S 4,11,31,90,254,728,2078,5931,16941,48360,138093,394288,1125795,
%T 3214477,9178177,26206271,74826094,213649101,610027119,1741795342,
%U 4973305753,14200157940,40545363081,115768182159,330550053876,943811471644
%N Number of n X 2 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 1 or 3 neighboring 1s.
%H R. H. Hardin, <a href="/A296572/b296572.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 4*a(n-2) + 3*a(n-3) + a(n-4) + 4*a(n-5) - a(n-6) - 6*a(n-7) - a(n-8) + a(n-9).
%F Empirical g.f.: x*(4 + 7*x + 4*x^2 + 3*x^3 + 3*x^4 - 6*x^5 - 7*x^6 + x^8) / (1 - x - 4*x^2 - 3*x^3 - x^4 - 4*x^5 + x^6 + 6*x^7 + x^8 - x^9). - _Colin Barker_, Feb 23 2019
%e Some solutions for n=5:
%e ..0..0. .1..0. .1..0. .0..0. .0..1. .1..1. .0..1. .0..0. .1..0. .0..1
%e ..0..0. .0..0. .0..0. .0..0. .0..1. .0..0. .1..0. .1..1. .0..0. .0..1
%e ..0..0. .0..1. .1..0. .1..0. .0..0. .1..1. .0..1. .0..0. .1..0. .1..1
%e ..0..0. .0..0. .0..0. .1..0. .0..0. .0..0. .1..0. .1..0. .0..1. .1..0
%e ..0..1. .0..0. .1..0. .0..0. .1..1. .0..0. .0..0. .0..0. .0..1. .1..0
%Y Column 2 of A296578.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 15 2017