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A241891 Total number of unit squares appearing in the Thue-Morse sequence of logical matrices (1, 0 version) after n stages.

%I A241891 #16 Jun 13 2015 00:55:01
%S A241891 1,2,4,8,20,72,244,968,3700,14792,58484,233928,932980,3731912,
%T A241891 14916724,59666888,238623860,954495432,3817806964,15271227848,
%U A241891 61084212340,244336849352,977344601204,3909378404808,15637502434420
%N A241891 Total number of unit squares appearing in the Thue-Morse sequence of logical matrices (1, 0 version) after n stages.
%C A241891 a(n) is the total number of isolated "1s" (no adjacent 1s in the horizontal or vertical directions) which appear as unit squares in the Thue-Morse sequence (another version starts with 1) of logical matrices after n stages. See links for more details.
%H A241891 Colin Barker, <a href="/A241891/b241891.txt">Table of n, a(n) for n = 0..1000</a>
%H A241891 Kival Ngaokrajang, <a href="/A241891/a241891.pdf">Illustration of initial terms</a>
%H A241891 Wikipedia, <a href="http://en.wikipedia.org/wiki/Thue%E2%80%93Morse_sequence">Thue-Morse sequence</a>
%H A241891 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,5,-20,-4,16).
%F A241891 a(n) = A033691(A001045(n)) for n > 2, a(0) = 1, a(1) = 2, a(2) = 4.
%F A241891 a(n) = 4*a(n-1)+5*a(n-2)-20*a(n-3)-4*a(n-4)+16*a(n-5). - _Colin Barker_, Jan 17 2015
%F A241891 G.f.: -(24*x^5+12*x^4+2*x^3-9*x^2-2*x+1) / ((x-1)*(x+1)*(2*x-1)*(2*x+1)*(4*x-1)). - _Colin Barker_, Jan 17 2015
%o A241891 (PARI) {a0=1;a1=2;print1(a0,", ",a1,", "); for (n=0,50, b=ceil(2*(2^n-1)/3); a=1-(-1)^b+4*b+2*b^2; if(Mod(n,2)==0, a=a+4); print1(a,", "))}
%o A241891 (PARI) Vec(-(24*x^5+12*x^4+2*x^3-9*x^2-2*x+1)/((x-1)*(x+1)*(2*x-1)*(2*x+1)*(4*x-1)) + O(x^100)) \\ _Colin Barker_, Jan 17 2015
%Y A241891 Cf. A010059, A241682.
%K A241891 nonn,easy
%O A241891 0,2
%A A241891 _Kival Ngaokrajang_, May 01 2014