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A259220 Number of (n+1) X (6+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

%I A259220 #18 Oct 09 2020 12:07:12
%S A259220 162,230,334,510,798,1278,2078,3422,5694,9566,16222,27774,48030,83934,
%T A259220 148286,264926,478686,874622,1615390,3014238,5678142,10789470,
%U A259220 20661854,39839870,77278878,150673118,295060798,579951582,1143447774,2260270206
%N A259220 Number of (n+1) X (6+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
%H A259220 R. H. Hardin, <a href="/A259220/b259220.txt">Table of n, a(n) for n = 1..210</a>
%H A259220 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-1,2).
%F A259220 a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).
%F A259220 G.f.: 2*x*(81 - 209*x + 31*x^2 + 128*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - _Colin Barker_, Dec 24 2018
%F A259220 From the above formulae, a(n) = 2*(2^n + 16*Fibonacci(n+3) + 31). - _Ehren Metcalfe_, Dec 27 2018
%e A259220 Some solutions for n=4:
%e A259220   0 1 0 1 0 1 0        0 1 1 1 0 1 1        1 1 0 0 1 1 1
%e A259220   0 1 0 1 0 1 0        1 0 0 0 1 0 0        0 0 1 1 0 0 0
%e A259220   0 1 0 1 0 1 0        1 0 0 0 1 0 0        1 1 0 0 1 1 1
%e A259220   0 1 0 1 0 1 0        0 1 1 1 0 1 1        0 0 1 1 0 0 0
%e A259220   1 0 1 0 1 0 1        1 0 0 0 1 0 0        1 1 0 0 1 1 1
%Y A259220 Column 6 of A259222.
%K A259220 nonn,easy
%O A259220 1,1
%A A259220 _R. H. Hardin_, Jun 21 2015