cp's OEIS Frontend

A208689 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

%I A208689 #8 Mar 07 2018 09:23:03
%S A208689 6,36,78,282,768,2430,7086,21588,64230,193554,579264,1740054,5216502,
%T A208689 15655428,46956702,140885610,422631744,1267935822,3803741790,
%U A208689 11411331636,34233822966,102701747106,308104791168,924315101862,2772944127078
%N A208689 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.
%C A208689 Row 3 of A208688.
%H A208689 R. H. Hardin, <a href="/A208689/b208689.txt">Table of n, a(n) for n = 1..210</a>
%F A208689 Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 3*a(n-3).
%F A208689 Conjectures from _Colin Barker_, Mar 07 2018: (Start)
%F A208689 G.f.: 6*x*(1 + 4*x - 3*x^2) / ((1 - 3*x)*(1 + x - x^2)).
%F A208689 a(n) = 2^(-n)*(5*6^(2+n) + (75-27*sqrt(5))*(-1+sqrt(5))^n + 3*(-1-sqrt(5))^n*(25+9*sqrt(5))) / 55.
%F A208689 (End)
%e A208689 Some solutions for n=4:
%e A208689 ..0..1..0..0....1..1..0..1....0..1..1..0....1..1..0..0....0..1..0..0
%e A208689 ..1..1..1..0....1..1..1..1....0..1..1..0....0..1..0..1....1..1..1..1
%e A208689 ..0..1..0..1....0..1..0..0....1..0..1..1....0..1..1..0....0..1..0..0
%Y A208689 Cf. A208688.
%K A208689 nonn
%O A208689 1,1
%A A208689 _R. H. Hardin_, Mar 01 2012