Search: id:A106400
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%I A106400
%S A106400 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A106400 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A106400 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%V A106400 1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,1,-1,-1,1,
               -1,1,1,-1,-1,1,
%W A106400 1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,1,-1,
               -1,1,-1,1,1,-1,
%X A106400 1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,1,
               1,-1,-1,1,-1,1
%N A106400 Thue-Morse sequence: let A_k denote the first 2^k terms; then A_0 = 1 
               and for k >= 0, A_{k+1} = A_k B_k, where B_k is obtained from A_k 
               by interchanging 1's and -1's.
%H A106400 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Fxtbook</a>
%F A106400 G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=v^3-2uvw+u^2w.
%F A106400 G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, 
               u3, u6)=u6*u1^3 - 3*u6*u2*u1^2 + 3*u6*u2^2*u1 - u3*u2^3.
%F A106400 Euler transform of sequence b(n) where b(2^k)=-1 and zero otherwise.
%F A106400 G.f.: Product_{k>=0} (1-x^(2^k)) = A(x) = (1-x)A(x^2).
%o A106400 (PARI) {a(n)=if(n<1, n>=0, a(n\2)*(-1)^(n%2))}
%o A106400 (PARI) {a(n)=local(A, m); if(n<1, n==0, m=1; A=1+O(x); while(m<=n, m*=2; 
               A=subst(A, x, x^2)*(1-x)); polcoeff(A, n))}
%Y A106400 Cf. a(n)=(-1)^A010060(n).
%Y A106400 Convolution inverse of A018819.
%Y A106400 Sequence in context: A000012 A008836 A064179 this_sequence A112865 A121241 
               A122188
%Y A106400 Adjacent sequences: A106397 A106398 A106399 this_sequence A106401 A106402 
               A106403
%K A106400 sign
%O A106400 0,1
%A A106400 Michael Somos, May 02 2005

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