Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Apr 17 2018 06:18:34
%S 4,22,124,694,3892,21814,122284,685462,3842404,21538774,120736732,
%T 676795894,3793814164,21266419702,119210006284,668237802454,
%U 3745841266372,20997505287574,117702592547644,659787917778742
%N 1/128 the number of (n+2) X 3 binary arrays with no 3 X 3 subblock trace equal to any horizontal or vertical neighbor 3 X 3 subblock trace.
%C Column 1 of A185866.
%H R. H. Hardin, <a href="/A185858/b185858.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 4*a(n-1) + 9*a(n-2).
%F Conjectures from _Colin Barker_, Apr 17 2018: (Start)
%F G.f.: 2*x*(2 + 3*x) / (1 - 4*x - 9*x^2).
%F a(n) = ((2 - sqrt(13))^n*(-4+sqrt(13)) + (2+sqrt(13))^n*(4+sqrt(13))) / (3*sqrt(13)).
%F (End)
%e Some solutions for 4 X 3:
%e ..0..0..0....1..0..0....0..1..1....0..0..0....0..0..1....0..1..0....1..0..0
%e ..0..1..1....0..1..0....0..1..1....1..0..1....1..0..1....1..1..0....1..1..0
%e ..0..0..1....0..0..1....0..1..0....0..0..0....0..1..1....0..1..0....0..0..1
%e ..0..1..0....0..1..0....0..1..1....1..0..0....1..1..0....1..0..0....1..0..1
%Y Cf. A185866.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 05 2011