cp's OEIS Frontend

A259243 Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0111.

%I A259243 #7 Dec 24 2018 16:21:26
%S A259243 9,21,48,111,255,588,1353,3117,7176,16527,38055,87636,201801,464709,
%T A259243 1070112,2464239,5674575,13067292,30091017,69292893,159565944,
%U A259243 367444623,846142455,1948476324,4486903689,10332332661,23793043728,54790041711
%N A259243 Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0111.
%H A259243 R. H. Hardin, <a href="/A259243/b259243.txt">Table of n, a(n) for n = 1..210</a>
%F A259243 Empirical: a(n) = a(n-1) + 3*a(n-2).
%F A259243 Conjectures from _Colin Barker_, Dec 24 2018: (Start)
%F A259243 G.f.: 3*x*(3 + 4*x) / (1 - x - 3*x^2).
%F A259243 a(n) = (2^(-n)*((1-sqrt(13))^n*(-7+2*sqrt(13)) + (1+sqrt(13))^n*(7+2*sqrt(13)))) / sqrt(13).
%F A259243 (End)
%e A259243 Some solutions for n=4:
%e A259243 ..1..0....1..1....1..0....0..1....1..0....1..1....1..1....1..0....0..1....0..1
%e A259243 ..1..0....1..0....1..1....1..1....1..1....0..1....0..1....1..1....1..1....1..1
%e A259243 ..1..1....1..0....0..1....0..1....0..0....1..1....0..1....0..1....1..0....0..0
%e A259243 ..0..0....1..1....1..1....1..1....1..1....0..1....1..1....1..1....1..1....1..1
%e A259243 ..1..1....0..1....0..0....0..1....0..0....0..1....0..0....1..0....1..0....0..0
%Y A259243 Column 1 of A259250.
%K A259243 nonn
%O A259243 1,1
%A A259243 _R. H. Hardin_, Jun 22 2015