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A259218 Number of (n+1) X (4+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

%I A259218 #13 Oct 09 2020 12:07:16
%S A259218 45,71,112,183,303,510,869,1499,2616,4619,8251,14910,27249,50343,
%T A259218 93968,177071,336567,644702,1243405,2412387,4704360,9213891,18112547,
%U A259218 35715038,70604793,139874255,277587904,551679879,1097703231,2186254014,4357699061
%N A259218 Number of (n+1) X (4+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
%H A259218 R. H. Hardin, <a href="/A259218/b259218.txt">Table of n, a(n) for n = 1..210</a>
%H A259218 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-1,2).
%F A259218 a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).
%F A259218 G.f.: x*(45 - 109*x + 8*x^2 + 64*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - _Colin Barker_, Dec 24 2018
%F A259218 a(n) = 2^(n+1)+8+11*A000045(n+3). - _R. J. Mathar_, Oct 09 2020
%e A259218 Some solutions for n=4:
%e A259218 ..1..1..1..1..1....1..1..1..1..0....0..1..0..0..1....0..1..0..1..1
%e A259218 ..0..0..0..0..0....0..0..0..0..1....0..1..0..0..1....1..0..1..0..0
%e A259218 ..1..1..1..1..1....0..0..0..0..1....0..1..0..0..1....1..0..1..0..0
%e A259218 ..0..0..0..0..0....0..0..0..0..1....0..1..0..0..1....0..1..0..1..1
%e A259218 ..1..1..1..1..1....0..0..0..0..1....0..1..0..0..1....1..0..1..0..0
%Y A259218 Column 4 of A259222.
%K A259218 nonn,easy
%O A259218 1,1
%A A259218 _R. H. Hardin_, Jun 21 2015