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A259219 Number of (n+1) X (5+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

%I A259219 #18 Oct 09 2020 12:07:28
%S A259219 85,127,192,303,487,798,1325,2227,3784,6499,11283,19806,35161,63135,
%T A259219 114656,210535,390703,732286,1385109,2641659,5075320,9814107,19083707,
%U A259219 37286398,73147297,143988103,284244240,562450047,1115129719,2214450654
%N A259219 Number of (n+1) X (5+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
%H A259219 R. H. Hardin, <a href="/A259219/b259219.txt">Table of n, a(n) for n = 1..210</a>
%H A259219 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-1,2).
%F A259219 a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).
%F A259219 G.f.: x*(85 - 213*x + 24*x^2 + 128*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - _Colin Barker_, Dec 24 2018
%F A259219 From the above formulae, a(n) = 2^(n+1) + 19*Fibonacci(n+3) + 24. - _Ehren Metcalfe_, Dec 27 2018
%e A259219 Some solutions for n=4:
%e A259219   0 1 0 1 0 1    1 1 1 1 1 1    1 0 0 0 0 0    0 0 0 1 1 1
%e A259219   0 1 0 1 0 1    0 0 0 0 0 0    0 1 1 1 1 1    1 1 1 0 0 0
%e A259219   0 1 0 1 0 1    1 1 1 1 1 1    1 0 0 0 0 0    0 0 0 1 1 1
%e A259219   0 1 0 1 0 1    0 0 0 0 0 0    0 1 1 1 1 1    1 1 1 0 0 0
%e A259219   1 0 1 0 1 0    1 1 1 1 1 1    1 0 0 0 0 0    0 0 0 1 1 1
%Y A259219 Column 5 of A259222.
%K A259219 nonn,easy
%O A259219 1,1
%A A259219 _R. H. Hardin_, Jun 21 2015