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

%I #18 Oct 09 2020 12:07:12

%S 162,230,334,510,798,1278,2078,3422,5694,9566,16222,27774,48030,83934,

%T 148286,264926,478686,874622,1615390,3014238,5678142,10789470,

%U 20661854,39839870,77278878,150673118,295060798,579951582,1143447774,2260270206

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

%H R. H. Hardin, <a href="/A259220/b259220.txt">Table of n, a(n) for n = 1..210</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-1,2).

%F a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).

%F 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 From the above formulae, a(n) = 2*(2^n + 16*Fibonacci(n+3) + 31). - _Ehren Metcalfe_, Dec 27 2018

%e Some solutions for n=4:

%e 0 1 0 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1

%e 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0

%e 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1

%e 0 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0

%e 1 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 1

%Y Column 6 of A259222.

%K nonn,easy

%O 1,1

%A _R. H. Hardin_, Jun 21 2015