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A259221 Number of (n+1) X (7+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

%I A259221 #18 Oct 09 2020 12:07:33
%S A259221 311,421,588,869,1325,2078,3319,5377,8804,14545,24225,40670,68843,
%T A259221 117557,202636,352813,620837,1104574,1987407,3616121,6651956,12365081,
%U A259221 23211193,43964734,83952995,161472013,312533724,608223317,1189192349,2334286430
%N A259221 Number of (n+1) X (7+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
%H A259221 R. H. Hardin, <a href="/A259221/b259221.txt">Table of n, a(n) for n = 1..210</a>
%H A259221 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-1,2).
%F A259221 a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).
%F A259221 G.f.: x*(311 - 823*x + 148*x^2 + 512*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - _Colin Barker_, Dec 24 2018
%F A259221 From the above formulae, a(n) = 2^(n+1) + 53*Fibonacci(n+3) + 148. - _Ehren Metcalfe_, Dec 27 2018
%e A259221 Some solutions for n=4:
%e A259221   1 0 1 0 1 0 1 0     0 0 1 0 0 0 0 1     0 1 0 1 0 1 1 1
%e A259221   1 0 1 0 1 0 1 0     0 0 1 0 0 0 0 1     1 0 1 0 1 0 0 0
%e A259221   0 1 0 1 0 1 0 1     1 1 0 1 1 1 1 0     0 1 0 1 0 1 1 1
%e A259221   1 0 1 0 1 0 1 0     0 0 1 0 0 0 0 1     1 0 1 0 1 0 0 0
%e A259221   0 1 0 1 0 1 0 1     1 1 0 1 1 1 1 0     0 1 0 1 0 1 1 1
%Y A259221 Column 7 of A259222.
%K A259221 nonn,easy
%O A259221 1,1
%A A259221 _R. H. Hardin_, Jun 21 2015