Search: id:A005590
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%I A005590 M0048
%S A005590 0,1,1,0,1,1,0,1,1,2,1,1,0,1,1,0,1,3,2,1,1,2,1,1,0,1,1,0,1,1,0,1,1,4,3,
%T A005590 1,2,3,1,2,1,3,2,1,1,2,1,1,0,1,1,0,1,1,0,1,1,2,1,1,0,1,1,0,1,5,4,1,3,4,
%U A005590 1,3,2,5,3,2,1,3,2,1,1,4,3,1,2,3,1,2,1,3,2,1,1,2,1,1,0,1,1,0,1,1,0,1,1
%V A005590 0,1,1,0,1,-1,0,1,1,-2,-1,1,0,1,1,0,1,-3,-2,1,-1,2,1,-1,0,1,1,0,1,-1,0,
               1,1,-4,-3,
%W A005590 1,-2,3,1,-2,-1,3,2,-1,1,-2,-1,1,0,1,1,0,1,-1,0,1,1,-2,-1,1,0,1,1,0,1,
               -5,-4,1,-3,4,
%X A005590 1,-3,-2,5,3,-2,1,-3,-2,1,-1,4,3,-1,2,-3,-1,2,1,-3,-2,1,-1,2,1,-1,0,1,
               1,0,1,-1,0,1,1
%N A005590 a(0) = 0, a(1) = 1, a(2n) = a(n), a(2n+1) = a(n+1)-a(n).
%C A005590 Sequence is 2-regular.
%C A005590 G.f. satisfies A(x)=(1+1/x-x)*A(x^2). - Michael Somos, Sep 17 2003
%D A005590 J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical 
               Computer Sci., 98 (1992), 163-197.
%D A005590 B. Reznick, A new sequence with many properties, Abstract 809-10-185, 
               Abstracts Amer. Math. Soc., 5 (1984), p. 16.
%D A005590 B. Reznick, Some extremal problems for continued fractions, Ill. J. Math., 
               29 (1985), 261-279.
%D A005590 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005590 T. D. Noe, <a href="b005590.txt">Table of n, a(n) for n=0..10000</a>
%H A005590 J.-P. Allouche and J. Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/
               Papers/as0.ps">The ring of k-regular sequences</a>, Theoretical Computer 
               Sci., 98 (1992), 163-197.
%H A005590 Michael Gilleland, <a href="selfsimilar.html">Some Self-Similar Integer 
               Sequences</a>
%H A005590 R. Stephan, <a href="http://arXiv.org/abs/math.CO/0307027">Divide-and-conquer 
               generating functions. I. Elementary sequences</a>
%F A005590 G.f.: x*prod(k>=0, 1+x^2^k-x^2^(k+1)). - Ralf Stephan, Apr 26 2003
%F A005590 Conjecture: a(3n)=0 iff n in A003714. - Ralf Stephan, May 2 2003
%F A005590 a(n)=sum{k=0..n-1, (-1)^A010060(n-k-1)*(binomial(k, n-k-1) mod 2)}; - 
               Paul Barry (pbarry(AT)wit.ie), Mar 26 2005
%p A005590 A005590 := proc(n) option remember; if n <= 1 then n; elif n mod 2 = 
               0 then A005590(n/2); else A005590((n+1)/2)-A005590((n-1)/2); fi; 
               end;
%o A005590 (PARI) a(n)=if(n<=1,n>0,if(n%2,a(n\2+1)-a(n\2),a(n/2))) (from Michael 
               Somos)
%Y A005590 Cf. A002487.
%Y A005590 Sequence in context: A145865 A076452 A076453 this_sequence A142598 A037800 
               A144411
%Y A005590 Adjacent sequences: A005587 A005588 A005589 this_sequence A005591 A005592 
               A005593
%K A005590 sign,nice,easy
%O A005590 0,10
%A A005590 N. J. A. Sloane (njas(AT)research.att.com).
%E A005590 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 
               28 2003
%E A005590 Signs corrected by Ralf Stephan, Apr 26 2003

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