A183330 - OEIS

%I #11 Apr 05 2020 21:27:53

%S 1,7,10,23,49,98,209,431,898,1871,3889,8098,16849,35063,72970,151847,

%T 316001,657602,1368481,2847839,5926402,12332959,25665121,53409602,

%U 111146401,231297767,481335050,1001667383,2084488849,4337860898

%N Number of n X 2 binary arrays with each 1 adjacent to exactly two 0's.

%C Column 2 of A183335.

%H R. H. Hardin, <a href="/A183330/b183330.txt">Table of n, a(n) for n = 1..200</a>

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

%F Empirical g.f.: x*(1 + 6*x + x^2 - 2*x^3) / (1 - x - 2*x^2 - x^3 + x^4). - _Colin Barker_, Feb 27 2018

%e Some solutions for 7 X 2:

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

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

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

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

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

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

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

%Y Cf. A183335.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 03 2011