A204078 - OEIS

%I #14 Jun 06 2018 06:01:56

%S 0,4,4,16,100,324,1296,5476,21316,85264,343396,1368900,5475600,

%T 21921124,87647044,350588176,1402502500,5609710404,22438841616,

%U 89756564836,359023862596,1436095450384,5744391388516,22977546380100,91910185520400

%N Number of nX2 0..3 arrays with every element neighboring horizontally or vertically both a 0 and a 1.

%C Column 2 of A204084.

%H R. H. Hardin, <a href="/A204078/b204078.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +4*a(n-2) +17*a(n-3) -2*a(n-4) -4*a(n-5) -16*a(n-6)

%F Empirical: a(n) = 4*round(2^n/7)^2  - _Mark van Hoeij_, May 14 2013

%F Empirical g.f.: 4*x^2*(1 - x - 2*x^2 - 4*x^3) / ((1 - x)*(1 - 4*x)*(1 + x + x^2)*(1 + 2*x + 4*x^2)). - _Colin Barker_, Jun 06 2018

%e Some solutions for n=5:

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

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

%e ..2..1....2..2....0..3....1..0....1..1....1..0....1..1....1..0....3..3....0..2

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

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

%Y Cf. A204084.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 10 2012