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A159782 a(0)=1; a(1)=a(2)=a(3)=a(4)=2; a(2n+1)=0 for n >= 2; a(4n)=a(4n-2) = a(n) + a(n+1) for n >= 2.

%I A159782 #22 May 22 2018 05:44:09
%S A159782 1,2,2,2,2,0,4,0,4,0,4,0,4,0,2,0,2,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,
%T A159782 4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,4,0,
%U A159782 4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4,0,4
%N A159782 a(0)=1; a(1)=a(2)=a(3)=a(4)=2; a(2n+1)=0 for n >= 2; a(4n)=a(4n-2) = a(n) + a(n+1) for n >= 2.
%C A159782 a(n) = {0, 1, 2 or 4}. - _Robert G. Wilson v_, May 27 2009
%C A159782 Also the number of palindromes of length n in the Thue-Morse sequence (A010060). - _Jeffrey Shallit_, Feb 19 2013
%H A159782 G. C. Greubel, <a href="/A159782/b159782.txt">Table of n, a(n) for n = 0..10000</a>
%H A159782 A. Blondin-Massé, S. Brlek, A. Garon, and S. Labbé, <a href="http://puma.dimai.unifi.it/19_2_3/4.pdf">Combinatorial properties of f-palindromes in the Thue-Morse Sequence</a>, Pure. Math. Appl., 19 (2-3) (2008), 39-52.
%t A159782 f[n_] := f[n]= Switch[ Mod[n, 4], 0, f[n/4] + f[n/4 + 1], 1, 0, 2, f[(n + 2)/4] + f[(n + 6)/4], 3, 0]; f[0] = 1; f[1] = f[2] = f[3] = f[4] = 2; Table[f@n, {n, 0, 104}] (* _Robert G. Wilson v_, May 27 2009 *)
%Y A159782 Cf. A010060.
%K A159782 easy,nonn
%O A159782 0,2
%A A159782 _Philippe Deléham_, Apr 22 2009
%E A159782 More terms from _Robert G. Wilson v_, May 27 2009