%I #8 Jan 03 2019 09:02:21
%S 33,2399,252097,29452071,3532758473,426525918799,51580839266577,
%T 6240392439847991,755059969459250713,91361403922865509599,
%U 11054703458723757804257,1337618299713909786621511
%N Number of (2n+1) X (3+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="/A263908/b263908.txt">Table of n, a(n) for n = 1..105</a>
%F Empirical: a(n) = 169*a(n-1) - 6387*a(n-2) + 71671*a(n-3) - 195052*a(n-4).
%F Conjectures from _Colin Barker_, Jan 03 2019: (Start)
%F G.f.: x*(33 - 3178*x + 57437*x^2 - 195052*x^3) / ((1 - 4*x)*(1 - 13*x)*(1 - 31*x)*(1 - 121*x)).
%F a(n) = (5*2^(1+2*n) + 11^(1+2*n) + 31*13^n + 29*31^n) / 81.
%F (End)
%e Some solutions for n=3:
%e ..0..0..1..1..1....0..0..1..1..1....0..1..1..0..1....0..1..0..1..0
%e ..0..0..1..1..1....0..0..0..0..1....0..0..1..1..1....1..0..1..1..0
%e ..1..1..1..1..1....1..1..0..0..1....1..1..1..0..0....1..1..1..1..1
%e ..1..1..1..1..1....0..1..0..1..0....0..1..0..1..0....0..1..1..0..1
%e ..1..1..1..0..0....1..0..0..1..1....1..1..0..0..1....0..0..0..0..1
%e ..1..1..1..0..0....1..0..0..1..1....1..1..1..1..1....0..0..1..1..1
%e ..1..1..1..1..1....0..1..0..1..0....0..0..1..1..1....1..0..0..1..1
%Y Column 3 of A263913 (nonzero terms).
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 29 2015