A297426 - OEIS

%I #8 Feb 28 2019 18:35:15

%S 1,7,14,22,68,163,320,782,1889,4109,9474,22365,50630,115709,268817,

%T 616265,1410697,3253586,7480630,17161490,39477589,90787636,208528864,

%U 479338273,1102090695,2532624372,5820869563,13380882748,30754476169

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

%H R. H. Hardin, <a href="/A297426/b297426.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(1 + 6*x + 7*x^2 + x^3 - 3*x^4 - 4*x^5) / (1 - x - 7*x^3 - x^5 + 4*x^6). - _Colin Barker_, Feb 28 2019

%e Some solutions for n=5:

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

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

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

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

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

%Y Column 3 of A297431.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 30 2017