A297390 - OEIS

%I #8 Feb 28 2019 07:44:16

%S 3,9,19,57,139,369,963,2489,6523,16929,44147,114953,299307,779697,

%T 2030243,5287833,13770971,35864001,93402579,243249193,633503627,

%U 1649849553,4296752131,11190160825,29142853947,75897603297,197662332211

%N Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

%H R. H. Hardin, <a href="/A297390/b297390.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(1 + 2*x)*(3 - 2*x^2) / (1 - x - 4*x^2 - 2*x^3 + 4*x^4). - _Colin Barker_, Feb 28 2019

%e Some solutions for n=5:

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

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

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

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

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

%Y Column 3 of A297395.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2017