%I #8 Jan 03 2019 09:03:21

%S 16,528,14112,359200,9024816,225934128,5650549312,141279105600,

%T 3532085249616,88302884507728,2207577385564512,55189471549212000,

%U 1379737047100994416,34493427986119721328,862335712313157059712

%N Number of (2n+2) X (2+2) 0..1 arrays with each row and column modulo 3 equal to 1, read as a binary number with top and left being the most significant bits.

%H R. H. Hardin, <a href="/A263907/b263907.txt">Table of n, a(n) for n = 1..105</a>

%F Empirical: a(n) = 33*a(n-1) - 207*a(n-2) + 175*a(n-3).

%F Conjectures from _Colin Barker_, Jan 03 2019: (Start)

%F G.f.: 16*x / ((1 - x)*(1 - 7*x)*(1 - 25*x)).

%F a(n) = (3 - 4*7^(1+n) + 25^(1+n)) / 27.

%F (End)

%e Some solutions for n=2:

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

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

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

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

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

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

%Y Column 2 of A263913 (nonzero terms).

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 29 2015