A183304 - OEIS

%I #10 Jan 27 2025 10:34:45

%S 1,4,9,19,42,93,205,452,997,2199,4850,10697,23593,52036,114769,253131,

%T 558298,1231365,2715861,5990020,13211405,29138671,64267362,141746129,

%U 312630929,689529220,1520804569,3354240067,7398009354,16316823277

%N Half the number of n X 3 binary arrays with no element equal to a strict majority of its horizontal and vertical neighbors.

%H R. H. Hardin, <a href="/A183304/b183304.txt">Table of n, a(n) for n = 1..200</a>

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

%F Empirical G.f.: x*(1+x)^2/(1-2*x-x^3). - _Colin Barker_, Feb 23 2012

%e Some solutions with a(1,1)=0 for 3X4

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

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

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

%Y Column 3 of A183312.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 03 2011