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A259217 Number of (n+1) X (3+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

%I A259217 #12 Oct 09 2020 12:07:07
%S A259217 24,40,66,112,192,334,588,1048,1890,3448,6360,11854,22308,42352,81042,
%T A259217 156160,302736,589966,1154844,2269096,4472514,8838760,17505576,
%U A259217 34732942,69015732,137303104,273427698,544948528,1086811680,2168631118,4329184620
%N A259217 Number of (n+1) X (3+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
%H A259217 R. H. Hardin, <a href="/A259217/b259217.txt">Table of n, a(n) for n = 1..210</a>
%H A259217 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-1,2).
%F A259217 a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).
%F A259217 G.f.: 2*x*(12 - 28*x + x^2 + 16*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - _Colin Barker_, Dec 24 2018
%F A259217 a(n) = 2^(n+1)+2+6*A000045(n+3). - _R. J. Mathar_, Oct 09 2020
%e A259217 Some solutions for n=4:
%e A259217 ..1..0..1..0....1..0..1..0....1..0..0..1....0..1..0..1....0..0..0..0
%e A259217 ..0..1..0..1....0..1..0..1....0..1..1..0....1..0..1..0....1..1..1..1
%e A259217 ..0..1..0..1....1..0..1..0....1..0..0..1....1..0..1..0....0..0..0..0
%e A259217 ..0..1..0..1....0..1..0..1....0..1..1..0....1..0..1..0....0..0..0..0
%e A259217 ..1..0..1..0....0..1..0..1....1..0..0..1....1..0..1..0....1..1..1..1
%Y A259217 Column 3 of A259222.
%K A259217 nonn,easy
%O A259217 1,1
%A A259217 _R. H. Hardin_, Jun 21 2015