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Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0 or 2 neighboring 1s.
1

%I #8 Feb 23 2019 04:21:34

%S 5,19,64,230,816,2895,10277,36480,129486,459622,1631463,5790997,

%T 20555577,72963551,258989554,919302704,3263133386,11582734875,

%U 41113779717,145936421820,518012193480,1838722844160,6526683619009,23166949384421

%N Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0 or 2 neighboring 1s.

%H R. H. Hardin, <a href="/A296330/b296330.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 4*a(n-2) + 5*a(n-3) + 2*a(n-4) - 2*a(n-5) - 3*a(n-6) - 2*a(n-7) + a(n-9).

%F Empirical g.f.: x*(5 + 9*x + 6*x^2 + x^3 - 5*x^4 - 5*x^5 - 2*x^6 + x^7 + x^8) / ((1 + x + x^2)*(1 - 3*x - 2*x^2 + 2*x^5 + x^6 - x^7)). - _Colin Barker_, Feb 23 2019

%e Some solutions for n=5:

%e ..0..0..1. .0..0..1. .0..1..0. .0..0..1. .0..1..0. .1..0..0. .1..1..0

%e ..1..0..0. .0..0..0. .0..0..0. .1..0..0. .0..0..0. .0..1..0. .1..0..0

%e ..0..0..0. .0..0..1. .1..0..0. .0..0..1. .1..0..0. .0..0..0. .0..0..0

%e ..1..0..0. .1..0..0. .0..0..1. .0..0..0. .0..0..0. .0..0..1. .1..0..0

%e ..0..0..0. .0..0..1. .0..1..1. .1..0..0. .0..0..0. .0..0..0. .0..1..0

%Y Column 3 of A296335.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 10 2017