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Number of n X 2 binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.
1

%I #10 Mar 27 2018 08:49:50

%S 3,6,13,27,57,119,250,523,1097,2297,4815,10086,21137,44283,92793,

%T 194419,407378,853559,1788481,3747361,7851867,16451910,34471669,

%U 72228171,151339401,317100335,664418698,1392152131,2916968489,6111905849

%N Number of n X 2 binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

%C Column 2 of A183322.

%C Is this related to A131246?

%H R. H. Hardin, <a href="/A183314/b183314.txt">Table of n, a(n) for n = 1..200</a>

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

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

%e Some solutions for 5 X 2.

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

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

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

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

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

%Y Cf. A131246, A183322.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 03 2011