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%I #8 Feb 23 2019 07:23:47
%S 1,5,16,37,96,254,654,1709,4472,11621,30257,78899,205534,535394,
%T 1395017,3634476,9468722,24669483,64272370,167449745,436262198,
%U 1136608103,2961236309,7714995835,20100110050,52367403411,136434332477,355456392933
%N Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 or 4 neighboring 1s.
%H R. H. Hardin, <a href="/A296536/b296536.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) - a(n-2) + 5*a(n-3) + a(n-4) + 6*a(n-5) + 7*a(n-6) + a(n-7) + 3*a(n-8) + 3*a(n-9) - 3*a(n-10) - 4*a(n-11) - a(n-12).
%F Empirical g.f.: x*(1 + 3*x + 7*x^2 + 5*x^3 + 12*x^4 + 8*x^5 + 4*x^6 + 6*x^7 - 7*x^9 - 5*x^10 - x^11) / ((1 + x^2 + x^3)*(1 - 2*x - 4*x^3 + x^4 - 2*x^5 - 4*x^6 + 3*x^8 + x^9)). - _Colin Barker_, Feb 23 2019
%e Some solutions for n=7:
%e ..0..1..1. .1..1..0. .0..0..0. .0..1..0. .0..0..0. .0..0..1. .0..1..0
%e ..0..1..0. .1..0..0. .1..1..0. .1..1..1. .1..1..0. .1..1..1. .1..1..1
%e ..0..0..0. .0..0..1. .1..0..0. .0..1..0. .1..0..0. .1..0..0. .0..1..0
%e ..1..1..0. .0..1..1. .0..0..1. .1..1..0. .0..0..0. .0..1..1. .1..1..0
%e ..1..0..0. .0..0..0. .0..1..1. .0..0..0. .1..1..0. .0..1..0. .0..0..1
%e ..0..1..0. .1..1..0. .0..0..0. .0..0..0. .1..0..0. .1..1..0. .1..1..1
%e ..1..1..0. .1..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .1..0..0
%Y Column 3 of A296541.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 15 2017
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