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%I #26 Apr 04 2019 17:28:34
%S 1,4,8,10,12,14,15,16,22,24,23,26,29,30,34,40,38,40,43,42,47,50,52,56,
%T 55,56,62,66,64,70,71,64,78,80,75,82,83,82,88,96,89,92,100,98,102,106,
%U 105,104,111,112,114,122,118,122,125,120,130,136,131,130,141,134,138,160
%N Convolution of Thue-Morse sequence A001285 with itself.
%C Comment from _Jeremy Gardiner_, Dec 28 2008: The following sequences all appear to have the same parity: A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975.
%H Seiichi Manyama, <a href="/A029886/b029886.txt">Table of n, a(n) for n = 0..10000</a>
%H Tanya Khovanova, <a href="http://arxiv.org/abs/1410.2193">There are no coincidences</a>, arXiv preprint 1410.2193 [math.CO], 2014.
%F G.f.: (1/4)*(3/(1 - x) - Product_{k>=0} (1 - x^(2^k)))^2. - _Ilya Gutkovskiy_, Apr 03 2019
%t P[n_, x_] := (bb = IntegerDigits[n, 2]) . x^Range[Length[bb]-1, 0, -1];
%t TM[n_] := 1 + Mod[P[n, 1], 2];
%t a[n_] := Sum[TM[k] TM[n-k], {k, 0, n}];
%t Table[a[n], {n, 0, 63}] (* _Jean-François Alcover_, Aug 31 2018 *)
%o (PARI) a(n)=sum(k=0,n,(1+subst(Pol(binary(k)),x,1)%2)*(1+subst(Pol(binary(n-k)),x,1)%2)) \\ _Ralf Stephan_, Aug 23 2013
%Y Cf. A001285.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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