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A259216 Number of (n+1) X (2+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

%I A259216 #12 Oct 09 2020 12:07:01
%S A259216 13,23,40,71,127,230,421,779,1456,2747,5227,10022,19345,37559,73288,
%T A259216 143615,282439,557126,1101709,2183123,4333408,8613683,17141395,
%U A259216 34143686,68062297,135760415,270931576,540909719,1080276751,2158057382,4312075957
%N A259216 Number of (n+1) X (2+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
%H A259216 R. H. Hardin, <a href="/A259216/b259216.txt">Table of n, a(n) for n = 1..210</a>
%H A259216 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-2).
%F A259216 a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3).
%F A259216 From _Colin Barker_, Dec 24 2018: (Start)
%F A259216 G.f.: x*(13 - 16*x - 16*x^2) / ((1 - 2*x)*(1 - x - x^2)).
%F A259216 a(n) = 2^(1+n) + (3*2^(-n)*((1-sqrt(5))^n*(-2+sqrt(5)) + (1+sqrt(5))^n*(2+sqrt(5)))) / sqrt(5).
%F A259216 (End)
%F A259216 a(n) = 2^(n+1)+3*A000045(n+3). - _R. J. Mathar_, Oct 09 2020
%e A259216 Some solutions for n=4:
%e A259216 ..0..1..0....1..0..1....1..0..1....0..1..0....0..1..0....1..1..1....1..0..1
%e A259216 ..1..0..1....0..1..0....1..0..1....1..0..1....1..0..1....0..0..0....1..0..1
%e A259216 ..0..1..0....1..0..1....0..1..0....1..0..1....0..1..0....0..0..0....0..1..0
%e A259216 ..1..0..1....0..1..0....0..1..0....1..0..1....0..1..0....0..0..0....0..1..0
%e A259216 ..0..1..0....1..0..1....0..1..0....0..1..0....1..0..1....1..1..1....1..0..1
%Y A259216 Column 2 of A259222.
%K A259216 nonn,easy
%O A259216 1,1
%A A259216 _R. H. Hardin_, Jun 21 2015